Chapter 11
Encryption: A Final, Brilliant Mistake
My email is mostly from students requesting homework help, plus a couple of receipts and tracking notices from online purchases …
While the concept of internet commerce seemed hopelessly exotic barely twenty years ago, buying things online has now become so much the norm that venerable chain stores have been pushed to and even over the brink of bankruptcy by the growth of web-based retail. You can buy almost anything on the internet these days, and for some people even a quick run out to buy milk has been replaced by pointing a web browser at an online grocery service.
Of course, e-commerce would be all but unthinkable without the ability to encrypt messages, enabling a customer to send credit card information to a retailer without worrying that it’s being shared with the entire world. Vast sums of money have been spent on technologies to secure commercial transactions over the internet, and the development of successful methods for sharing financial information is largely responsible for the explosive growth of online markets.
This may seem an odd topic for a book focused on the quantum, because at the moment the security of online transactions is guaranteed by purely classical means. But as we complete our exploration of the physics of everyday reality, we’ll take one brief detour into the speculative. The quantum cryptography technology I’ll describe in this chapter is not widely used … yet.
These techniques are very real, though, and becoming more practical every day. In the fall of 2017, researchers in Beijing and Vienna demonstrated quantum-secured communication via a Chinese satellite, opening a research conference with a phone call between China and Austria that was encrypted with a quantum key. Widespread global quantum communication is not far off, despite the fact that it has its roots in some of the most exotic physics ever discovered.
Quantum cryptography draws on the idea of “entanglement,” arguably the most troubling of all the weird properties of quantum mechanics. Quantum entanglement establishes connections between particles at great distances, an idea that Einstein famously derided as “spooky action-at-a-distance.” Numerous experiments since the 1970s have demonstrated the reality of this phenomenon, though, forcing physicists to grapple with the deeper meanings of space, time, and the transfer of information.
At first glance, the questions entanglement raises may seem primarily philosophical, but in fact they have deeply practical applications. If you’re trying to transmit messages from one person to another without anyone else being able to read them, this “spooky” connection between entangled particles turns out to be exactly what you want.
The Secret to Keeping Secrets
The central problem of cryptography has probably been around as long as written language. The most obvious way to keep secrets is, of course, to only share them face to face, but such meetings are not always practical. One solution is the use of codes: writing a message in a way that’s intelligible to the intended recipient, but gibberish to anyone who intercepts it.
There are numerous ingenious code systems dating back thousands of years, but we’re interested in modern security, which is best understood in terms of math. In modern cryptosystems, the secret message is converted into a string of numbers, and then some mathematical operation is performed on those numbers by the sender, resulting in a different string of numbers that is sent openly to the recipient. If the recipient knows exactly what was done, they can undo it, recovering the original message; anybody else will be left with a string of nonsense.
To give a concrete but rudimentary example, imagine doing the conversion from letters to numbers by simple substitution: A = 01, B = 02, all the way to Z = 26. If we want to encode the word “BREAKFAST,” we end up with
For a mathematical operation to obscure this, we take a random string of 1s and 0s as our cipher key, one for each letter of the message. We then combine the two, adding one to the original number if our key has a 1 in that spot, and subtracting one if our key has a 0.
A person receiving the cipher text “ASDZJEBTS” without knowing the code would most likely conclude that the sender’s cat was walking on the keyboard again. If the intended recipient has the key and knows the appropriate sequence of operations, though, they can reverse the encryption—adding 1 for a zero in the key, subtracting 1 for a one in the key—and recover the original message.
This simple cipher illustrates the basic principle, which is also the chief problem: it depends on both sender and recipient knowing the right sequence of operations to apply, according to a shared key—in this case, 010000110. If the recipient doesn’t have the same key as the sender, they’re no more able to decode the message than some random eavesdropper.
The simplest way around this is to use a single key all the time, so both sender and receiver only need to share and remember one special set of digits. Unfortunately, with enough ciphered message text to work from, mathematical analysis can determine the key and recover the secret message, given enough time. “Enough time” may be a lot—for a long enough key, the time required to be sure of deciphering a message with current methods on existing computers can be longer than the age of the universe. This is what most internet messages rely on: they use a single shared key with enough digits that it’s exceedingly unlikely that anyone will figure it out fast enough to do harm. This sort of cryptography is vulnerable to improvements in computing power or new mathematical techniques, though—a person with a better decryption program and bad intentions can potentially decrypt vast amounts of material.
A more secure method is to have a list of random numbers to use as keys—a so-called “one-time pad”—and use a new one to encode each message, but this creates additional logistical hassle for the sender and receiver. Each must have access to some large shared list of random numbers, and the longer the list of numbers that needs to be shared, the harder it is to keep them secret.1 It can also be difficult to securely replenish the list after many messages if the sender and recipient are in places where they can’t easily meet.
The ideal system for this sort of cryptography would be one that somehow generated random numbers on demand. But while there are plenty of random processes either sender or recipient could use to generate a useful key, if they’re doing the generation in two different places, the numbers produced will necessarily be different, and thus useless for encoding text. The need for the sender and receiver’s numbers to be identical makes on-demand key generation all but impossible.
At least, all but impossible in classical physics. Quantum mechanics, though, provides a loophole that allows you to generate a truly random number that is nonetheless shared by two people in two different locations. It works thanks to one of the thorniest philosophical issues raised in quantum physics, the one that drove Einstein out of the field he had helped invent.
Dicing with the Universe
One of the most frequently shared Einstein quotes is usually rendered as something like, “God does not play dice with the universe.” This traces back to a remark first made to Max Born in a 1926 letter: “[Quantum mechanics] says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.”2
The fundamental issue here has to do with the probabilistic nature of quantum mechanics, first stated by Born: quantum wavefunctions tell us only the probability of particular measurement outcomes. If we repeat an experiment many, many times, and aggregate all the results, the wavefunction will be an excellent description of the full range of results. Knowing the wavefunction, however, does not allow us to predict the exact outcome of any particular run of the experiment; as far as we can tell, the result of a single experiment on a quantum particle is completely random.
This randomness poses a serious philosophical problem. Probability per se is not the issue, even for Einstein himself—as we’ve seen, some of his greatest contributions to physics involved using statistical methods to predict the behavior of vast numbers of particles without needing to consider the details of any individual particle’s behavior. In those cases, though, he could presume that the randomness was just covering for a lack of knowledge about the detailed interactions. A deeper theory that would predict specific results for individual particles remained a possibility, in which case the statistical methods would just be a convenience, a tool for avoiding the impossible task of calculating the details of the interactions between huge quantities of individual particles. We do this with purely classical systems all the time—knowing the initial position and velocity of a roulette ball and wheel would in principle allow you to predict exactly where the ball will stop, but in practice, that calculation is too difficult, and instead we can treat the game as purely random and discuss the outcome in terms of probability.
As quantum mechanics began to emerge, though, it became clear that, in quantum mechanics, randomness is fundamental. The inability to predict the outcome of a single quantum experiment isn’t just some technical glitch, it’s inherent. In the quantum theory formulated by Heisenberg and Schrödinger, and interpreted by Bohr and Born and Pauli, it simply does not make sense to talk about specific properties of individual particles. The Heisenberg uncertainty principle (Chapter 7) isn’t describing a technical issue with the way we measure position and momentum; it reflects the fact that it’s simply impossible to have a well-defined position and momentum for a particle that also has wave nature.3
The younger generation of physicists, Pauli and Heisenberg and their cohort, were largely willing to accept this as the cost of doing business, and reveled in the ability of the new theory to accurately predict the results of experiments that had baffled physicists for years. Some older physicists, though, were deeply troubled by this fundamental randomness, and sought a replacement theory that would be more deterministic.4 This group included some of the physicists who’d been instrumental in the launching of quantum mechanics in the first place, most notably Einstein and Schrödinger.
This is the context of Schrödinger’s infamous cat thought experiment: he was highlighting what he saw as a problem for quantum theory, relating to this fundamental indeterminacy. While the question he raised did not deter the further development of quantum mechanics, the arguments it inspired have helped generate new and productive areas of research. Einstein’s objection, in the form of another thought experiment, was to prove even more fruitful.
Quantum Physics and Betteridge’s Law of Headlines
In the late 1920s, Einstein had a celebrated series of debates with Niels Bohr about interpretations of quantum physics, at the Solvay conferences of 1927 and 1930. The initial arguments focused on the uncertainty principle, which Einstein initially objected to because it went against classical intuition. While Einstein eventually reconciled himself to the idea of the uncertainty principle, and moved on to a deeper objection, Bohr continued to interpret his arguments in that light, meaning that a lot of their celebrated arguments are actually two brilliant physicists talking past each other.
Einstein’s final and most significant contribution to the still-ongoing argument about the foundations of quantum mechanics came in a 1935 paper written with his younger colleagues Boris Podolsky and Nathan Rosen. The “EPR” paper caught Bohr and many other physicists who were used to regarding Einstein’s arguments as uncertainty-based totally by surprise, because it more clearly explained his real objection, and pointed at a deeper issue with quantum theory.5
The paper is titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” There’s an old joke among journalists, “Betteridge’s Law of Headlines,” holding that any story whose headline is a question can be answered with the single word: “No.” The EPR paper is no exception: Einstein and his colleagues considered an unusual physical system to argue that quantum theory as developed and interpreted by Bohr and his colleagues in Copenhagen could not capture all of physical reality. This was the formal introduction of “entanglement” to physics,6 and the concept has troubled physicists ever since.
The original EPR argument involves the position and momentum of two particles, but the argument is clearer when applied to a two-state system like the spin of an electron. As we saw in the Stern-Gerlach experiment (Chapter 6), you can use a magnetic field to separate a bunch of electrons into two groups: one with the spin pointing “up” (along the magnetic field), the other with the spin pointing “down” (opposite the field).
The orientation of the Stern-Gerlach magnet is an arbitrary thing, though—up and down are not well-defined directions in space, and you could perfectly well tip the whole apparatus on its side and get the same basic result: half of the electrons will be “spin-left,” and half “spin-right.” If you start with a random sample of electrons, and a randomly chosen magnetic field direction, you’ll always get two groups. If you select one of the groups and repeat the measurement, passing it through the same magnetic field a second time, the results remain the same as well: all the spin-up electrons will stay spin-up (or the spin-left ones will stay spin-left), and vice versa.
An obvious extension of this experiment is to take one of the two groups separated by one Stern-Gerlach magnet—spin-up, say—and feed it into a second magnet with a different orientation—say, left-right. When you do this, you’ll again find two groups—for instance, half of the spin-up electrons will be spin-left, and half spin-right. The same is true if you do left-right first, then up-down, or any combination of two magnet sets where the second is rotated by 90 degrees.
So far, so good, but things get weird when you add a third magnet. Common sense would seem to say that if you take the group of electrons that were spin-up in the first magnet and spin-left in the second, then pass them through a second up-down magnet, you should find all of them in the spin-up group. After all, they were already measured to be spin-up.
That’s not what happens, though. The electrons that were first spin-up and then spin-left will separate into two equal groups: half spin-up, and half spin-down. Somehow, the process of measuring these electrons as spin-left has erased the original spin-up result, returning you to a random outcome for the up-down measurement.7
In the mathematical description of spin worked out by Pauli, the reason for this is simple: the up-down and left-right measurements of an electron’s spin are complementary to each other in the same way that measurements of its position and momentum are. They’re subject to an uncertainty principle–like relationship, and it simply does not make sense to talk about the up-down and left-right states of an electron’s spin as having well-defined values at the same time.
The EPR paper, though, uses a system of two particles to argue that this quantum indeterminacy cannot be a complete description of reality. They imagined a state of two particles whose individual state was indeterminate, but whose combined state had a definite value. In the spin framework, this would mean knowing that the two particles have opposite spins—one up and one down, or one left and one right—but not which is which. (This is not difficult to arrange—you get this kind of state, for example, from a reaction that breaks a diatomic molecule in two.) They then imagined separating these two particles by a substantial distance before measuring their individual properties.
The correlation means that when the scientist in possession of particle A (traditionally named “Alice” in discussions of cryptography) measures spin-up, they can predict with absolute certainty that particle B (held by Alice’s colleague Bob) will be found to be spin-down. They can’t say in advance which will be which, but the correlation between the results is absolute, and knowing the state of one particle instantly tells you the state of the other.
If we stick with a single measurement, this isn’t particularly surprising even from a classical standpoint. If I take the queen of spades and the jack of diamonds from a deck of cards, and mail them in sealed envelopes to different locations, when Alice opens her envelope to find the queen of spades, she knows instantly that Bob has the jack of diamonds, no matter where he is. The randomness in this case reflects merely a lack of knowledge about the state, not any inherent indeterminacy: each envelope contains a specific card the whole time it’s making its way through the postal system—we just don’t know which is which.
In the spin case, though, we’re not restricted to a single measurement, but could choose between two complementary measurements—if Alice had instead chosen to measure left-right, an outcome of spin-left would let them know with absolute certainty that Bob had spin-right. The randomness here is not a simple lack of knowledge in the classical sense, but rather a more fundamental indeterminacy. It’s as if I mailed two cards from a deck, and opening the envelope from the top would reveal either the queen of spade or jack of diamonds, while opening the envelope from the end would reveal either the ace of hearts or the two of clubs. In this case, we’re not only unsure of what specific card is in each envelope, it’s not even clear what the options are until the envelope is opened.
But, as Einstein, Podolsky, and Rosen pointed out, the particles have no way of knowing beforehand which measurement to expect, left-right or up-down, and there’s no restriction on the timing of the measurements that would allow for a message to pass from A to B to tell the other particle which outcome to choose. And yet, the correlations between measurements must be maintained. To Einstein, this suggested that all of the possible measurement outcomes must be determined in advance, each particle carrying with it a set of instructions for what result to show for any given measurement. Such a list of results, though, would go against the idea of quantum indeterminacy—each individual particle really would have a definite state the whole time, with the measurement results determined by some hidden variable not described in quantum mechanics, but potentially able to be determined with some deeper, more complete theory.
The only alternative would be what Einstein derisively referred to as “spukhafte fernwirkung,” a “spooky action-at-a-distance” communicating the result of Alice’s measurement to Bob’s particle at speeds far exceeding the speed of light. Such a linkage between widely separated particles would violate basic intuitions about space, time, and information as described by the theory of relativity. That sort of “non-local” interaction would create such enormous problems for classical physics—if you could send information faster than light, you could even create a paradox where effects happen before their causes—that Einstein rejected it out of hand.
Einstein to Bell to Aspect
The EPR paper, in the words of one of Bohr’s close colleagues, Leon Rosenfeld, “came down upon us as a bolt from the blue.” The Copenhagen circle of physicists had not anticipated this line of argument, and struggled to understand it. Bohr rushed out a paper in response with the same title, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, but this mostly served to muddy the waters; Bohr was not a clear writer at the best of times, and was caught badly off guard by the EPR thought experiment.
Over time, the response coalesced into a challenge to one of the central premises of the EPR argument, namely that the measurement at point A is made “without in any way disturbing” the measurement to be made at point B. In Bohr’s words, the fact that the two particles are entangled into a single quantum state means that Alice’s measurement exerts “an influence on the very conditions which define the possible types of predictions regarding the future behavior” of Bob’s particle. According to the Copenhagen interpretation, the complete quantum description of reality inherently incorporates all the measurements that will or might be made at widely separated locations.
This approach to entanglement didn’t really make anybody happy, but the situation seemed so arcane and artificial that most physicists didn’t give it much thought. Quantum mechanics was spectacularly successful at calculating the properties of a huge number of interesting systems, and most physicists focused their energy on those calculations, not an odd philosophical dispute between Einstein and Bohr that nobody could address in an experiment. Both camps were in agreement about what the measurable results of an EPR-type experiment would be; they disagreed only about the “why” of those results—whether the outcome was truly indeterminate but entangled, or determined in advance by hidden variables. Bohr’s view drew extra support from an assertion by John von Neumann that a “hidden variable” theory was mathematically impossible; von Neumann turned out to be flatly wrong on this point, but he was so respected that many physicists who were inclined to Bohr’s view simply accepted his claim without checking the math.
This muddled philosophical impasse remained for almost thirty years without a breakthrough. Einstein and Schrödinger basically gave up on quantum theory, moving on to other fields,8 and quantum mechanics continued to develop on the lines laid out by Bohr and his Copenhagen colleagues. In the mid-1960s, though, an Irish physicist named John Bell took a careful look at the Einstein, Podolsky, and Rosen argument, and realized that there was a way to experimentally distinguish between the “local hidden variable” theories they preferred and the orthodox quantum explanation.
The key to Bell’s trick is to look at what happens when Alice and Bob make different measurements. If the two spin detectors are set to make the same measurement—both looking for up-down, or both left-right—then the results will be simply correlated, and there’s nothing more you can do with that. If they’re looking at different properties, though—one up-down and the other left-right, say—then there’s some probability of getting each of the possible combinations. And the range of possible probabilities is different for the local hidden variable theories than it is for quantum mechanics.
The essence of the local hidden variable approach is that each particle must carry with it a set of instructions as to what result it should return for each of the possible measurements that might be made on it. To make this more concrete, we can assign values of “0” and “1” to the two different possible outcomes (“1” for spin-up and “0” for spin-down, say), and consider three different possible settings for the angle of the detector relative to the up-down direction. (Three measurement options is the smallest number that provides enough mathematical complexity to illustrate Bell’s theorem; in reality, there are an infinite number of possible choices, requiring tricks from calculus to handle the enumeration.) A local hidden variable theory then allows pairs of particles to exist in eight possible states, which we can enumerate in a table:9
Each row shows a possible state for a particle pair, and the measurements returned for each detector setting. The “A” columns indicate the results of the measurements made by Alice at each of the three settings, the “B” columns those made by Bob. Any pair of entangled particles used in the experiment must be in one of these eight states, chosen at random.
To understand Bell’s argument, we put ourselves in the role of “Setter of Variables,” choosing the state of each entangled pair in an attempt to match the predictions of quantum mechanics. We’re free to adjust the probability of each of these eight states occurring, subject to the constraint that a collection of repeated measurements by any single detector at any of the settings must always have a 50 percent chance of returning “0” and a 50 percent chance of returning “1”.
As you can see, when both detectors have the same setting, the results are always opposite, reflecting the entanglement between the particles, so that part of the variable-setter’s job is easy. As Bell pointed out, though, a trickier question to consider is what happens when the two detectors are rotated to different angles. We want our hidden-variable approach to match the quantum predictions, whatever they may be, so we need to work out the maximum and minimum probability of getting opposite results at A and B for any pair of different settings.
It’s relatively easy to see how to make the maximum probability outcome, which is 100 percent: simply put half of the entangled pairs in state I and the other half in state VIII. For each of those states, no matter how Alice sets her detector, a 1 for her will be paired with a 0 for Bob, and vice versa.
To get the minimum probability, we obviously need to exclude those two states; if you look closely at the remaining six, you will see that there are always exactly two states that give opposite results for any particular pair of detector settings. If we use the combination A1 and B2, states II and VII give opposite outcomes, for example; if instead we picked A2 and B3, states IV and V would do the job. If those six states are equally likely, as they must be to ensure a 50/50 chance of 0 or 1 for each individual detector, we have a one-in-three chance of getting opposite results.
The probability of getting opposite results with different settings, then, must range from a maximum of 100 percent to a minimum of 33 percent. As the Setter of Variables, we can make our local-hidden-variable source match the behavior of quantum-entangled particles for any scenario, provided that the probability of opposite measurement results never drops below one in three.
So, what is the quantum prediction that the Setter of Variables needs to match? In the quantum picture, the measurements are not independent: in one way of speaking about it, when Alice sets her detector to A1 and gets a result of 1, Bob’s particle is definitely placed into the 0 state for that detector setting. If the entangled particles are spins, the exact probability of Bob getting a 0 for his particle at a different detector setting will then depend on the exact angle between the settings. If we know that Bob’s particle is in a state that will give a result of 0 for the angle that corresponds to Alice’s setting A1, the probability of Bob detecting a 0 at setting B2 will be 100 percent if B2 is the same as A1, and decreases as B2 is rotated to a larger angle away from A1. Working through the details shows that the probability can be as low as 25 percent (for an angle of 60 degrees between detectors).
So, the Setter of Variables has an impossible task: for some combinations of detector settings, the probability of opposite measurements predicted by quantum physics is lower than the minimum probability that can be arranged using local hidden variables. What’s more, a careful experiment can readily distinguish between a probability of 25 percent and one of 33 percent, allowing physics to settle the argument between Bohr and Einstein once and for all.
Of course, reality is more complicated than our eight-state toy model, but then, so was Bell’s argument. Bell considered a much more general case, and proved an airtight mathematical theorem showing that for any EPR-type experiment, there will always be some choice of detector settings that makes predictions that local hidden variable theories simply cannot match.
Bell’s initial papers about the EPR experiment didn’t attract wide notice, but caught the interest of some physicists who decided to do the experiment. An initial test in the mid-1970s led by John Clauser found a result that agreed with the quantum prediction, though with weak statistical power. In 1981and 1982, a young French physicist named Alain Aspect did a series of experiments that are widely regarded as definitive, getting results that agreed with the quantum limit, and closing some obvious loopholes that might’ve allowed a local hidden variable theory to mimic the quantum result.10 Over the last thirty-five years, numerous additional “Bell test” experiments have been carried out, and all of them show the same thing: the quantum prediction is correct. The local hidden variable approach Einstein, Podolsky, and Rosen favored cannot be the correct description of our quantum universe.
Quantum Cryptography
To physicists, the most fascinating thing about the EPR argument and Bell’s theorem is what it tells us about the fundamental nature of the universe—these “spooky” correlations between entangled particles are very real, and confirmed in countless experiments. This means that distant points can have a quantum connection between them, which seems to run counter to our intuition that widely separated locations are, in fact, separate. Working out the details of this fundamental non-locality and what prevents it from manifesting more widely and upending our normal reality is a fascinating subject occupying a small but active community of physicists and philosophers.11
In this book, though, we’re mostly concerned with how aspects of quantum physics impact ordinary, everyday activities, and as fascinating as quantum foundations research may be, perhaps the most notable thing about quantum entanglement is its absence from everyday reality. In an everyday context, we simply don’t see it producing obvious practical effects.
There is one extremely practical application of quantum entanglement, though: its use in quantum cryptography. You can see this by looking at the raw data for any experiment on entangled particles: each individual measurement at point A will give a 0 or a 1 at random, but the scientist making those measurements will know with absolute certainty that their compatriot at point B making the same measurement has the opposite. The process allows two widely separated people to generate two lists of perfectly random numbers that are nevertheless perfectly correlated. That’s exactly what you need to encrypt and decrypt secret messages.
A twist based on real Bell-test experiments also allows our secretive physicists to rule out the possibility of eavesdropping, by switching between different detector settings while measuring their shared particles. Alice and Bob share a large number of entangled particle pairs (which we’ll continue to talk about as if they’re electron spins), and as they work through the list, they make a random decision whether to measure up-down or left-right. After making all their measurements, Alice openly shares the list of what measurement she made to each spin—not the value, just whether it was up-down or left-right. Roughly half of the time, Bob will have made the same measurements, and their results will be perfectly correlated—a “1” for Alice is a “0” for Bob, and vice versa. If Bob tells Alice which measurements were the same—not the outcome, just which pairs had the same detector settings—they get a set of perfectly correlated random numbers. When Alice finds a “1” in that half of the data, she can infer that Bob has a “0” and vice versa, and they can use those digits to make the key they need to encrypt their message.
The random switching between measurements slows the rate at which they generate bits for their key, but it foils would-be eavesdroppers. To have any chance of stealing the key, Alice’s archenemy Eve needs to intercept one of the entangled particles, and make her own measurement of its state before sending Bob a replacement particle in the definite state corresponding to her measurement result—if she measures spin-up and gets a result of “1,” she prepares a new particle in the “1” state, and sends it on to Bob. Since Eve has no way of knowing what measurement will be made, though, she has to choose her detector settings randomly as well, and this will inevitably introduce errors: if Eve measured up-down while Alice and Bob measured left-right, there’s a 50 percent chance that they’ll end up with two 1s rather than the 1-0 pair they expect.
Eve’s attempt to intercept the key will thus introduce errors, meaning that the attempt to decrypt the message will produce some gibberish characters. More importantly, it allows Alice and Bob to detect Eve’s presence—they can measure many more pairs than they need for the key, and then pick some random sections of that list as a test, sharing not just what measurement was made, but the outcome of the measurement. If Alice and Bob find too many cases where the correlation is imperfect, they know Eve is trying to intercept their key, and can take steps to eliminate the threat.
Illustration of quantum key generation. Alice and Bob share entangled spins, and each randomly decides whether to measure spin-up/spin-down or spin-left/spin-right. When their measurement choices match (shaded boxes), a “0” for Alice means a “1” for Bob, and vice versa. If they share what measurement they made for each spin, and keep the results for spins where they made the same measurement, they get correlated random numbers that they can use as a cryptographic key.
In practice, of course, there are many technical details that complicate the basic process just outlined. Real-world quantum cryptography systems use polarized photons as their entangled quantum particles, and reliably sending and detecting single photons can be very challenging. This has been an active area of research since the first proposals in 1984, though, and steady progress has been made. Quantum key distribution using polarized photons sent via optical fiber has been demonstrated at distances of several hundred kilometers, and is reliable enough that commercial systems are available.
The Chinese team mentioned earlier in the chapter has also demonstrated quantum key distribution between ground-based labs and a satellite in orbit. In the fall of 2017, they conducted that first “quantum-secured” international call between China and Austria via a Chinese satellite (named “Micius,” after the Latinized name of a Chinese scholar from the fifth century bce). As Micius passed above the lab in Beijing, they aimed laser pulses at the satellite to generate a key. A short time later, as the satellite passed over Vienna, they repeated the process with a lab there. The resulting joint key was then used to encode and decode a video link between the two cities to open a conference on quantum research with a video call between Chunli Bai, the president of the Chinese Academy of Sciences, and Anton Zeilinger of the Austrian Academy of Sciences.
While quantum key distribution systems are not yet in wide use, it’s not hard to believe, given the ever-increasing importance of online commerce, that banks and retailers will someday be using quantum entanglement to protect your purchases. Of course, that doesn’t completely guarantee security—there are also research groups studying “quantum hacking,” looking at tricks would-be eavesdroppers can use to disguise themselves and steal quantum keys. Quantum mechanics won’t end the arms race between those trying to keep secrets and those trying to steal them; it will just shift the fight to new and spookier ground.
A Brilliant Mistake
Einstein’s turn away from quantum physics after his pivotal role in inventing it was long regarded as an unfortunate footnote to a brilliant career. Abraham Pais’s magisterial scientific biography of Einstein, Subtle Is the Lord…, barely touches on the EPR paper, treating it as a brief and unfortunate late-career episode.
Ironically, Pais’s book was published in 1982—also the year when Alain Aspect’s third experiment using entangled photons was published, widely regarded as one of the best real-world realizations of the EPR scenario. That experiment showed fairly conclusively, thanks to the work of John Bell, that quantum-entangled particles are correlated in ways that simply cannot be explained with the sort of local hidden variable theory that would’ve satisfied Einstein. Since that time, the stature of the EPR paper has grown enormously. A 2005 analysis showed that the EPR paper was cited just 36 times before 1980, but 456 times between 1980 and 2005. In late 2017, the online article shows more than 5,900 citations.
In the end, the argument presented by Einstein, Podolsky, and Rosen turned out to be wrong, but not boringly so. In fact, it’s a brilliant mistake, bringing to light a strange and troubling aspect of quantum physics that had not previously been considered. It’s wrong in deep and subtle ways, and working out exactly how and why such a seemingly common-sense approach to physics fails has inspired an enormous amount of progress, in both the philosophy of physics and the technology used to probe the fundamental weirdness of entanglement.
In that sense, then, the EPR paper is not an unfortunate footnote to Einstein’s career in quantum physics, but a fitting end to it. He helped launch the field in 1905 with the bold claim that light could be a particle, and the dramatic introduction of entanglement thirty years later was an equally bold stroke, albeit in the opposite direction. Each of those papers, in its own way, transformed our understanding of the universe, showing the deep strangeness that exists in the foundations of our ordinary, everyday reality.
Notes
1 It’s easy to memorize or hide a short list of numbers, but the longer the list, the harder it is to keep track of in a non-obvious way. The problem is rather like the way most people can easily remember short but not very secure passwords, but longer, more secure strings of numbers and letters end up written on Post-It Notes stuck to the monitor, completely defeating their purpose.
2 The original was, of course, in German: “Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, dass der Alte nicht würfelt.”
3 The de Broglie-Bohm pilot wave approach is an alternative approach to quantum theory where individual particles do have definite properties, but are guided by an additional field that takes on most of the weirder properties associated with quantum particles. The specific initial properties of any individual particle are still randomly determined and impossible to measure, though, so the results of a single run of a quantum experiment remain unpredictable.
4 A deterministic alternative to quantum physics remains a topic of interest for a handful of researchers, most notably Gerard ‘t Hooft (who shared the 1999 Nobel Prize in Physics for work on the Standard Model), but subsequent generations mostly have followed the lead of Pauli and Heisenberg and prefer, in the tongue-in-cheek phrasing of David Mermin, to “shut up and calculate.”
5 It’s not a perfect presentation, though. In his later years, Einstein reportedly said that he was dissatisfied with the final wording of the EPR paper, which was largely written (in English) by Rosen.
6 The term “entanglement” was coined by Schrödinger, who shared Einstein’s misgivings.
7 Information about the original state is completely lost only for the case where the magnets are rotated by 90 degrees. If you choose an intermediate angle, you get two groups, with different probabilities—rotating the second magnets by 60 degrees from spin-up, say, gives a 75 percent–25 percent split between spin-right and spin-left. This will become important later.
8 Einstein devoted the last decades of his life to a fruitless search for a theory that would combine gravity and electromagnetism into a unified field. Schrödinger worked on field theory as well, and also wrote an influential book on the physics of living systems.
9 This approach to illustrating Bell’s theorem ultimately traces back to David Mermin.
10 The details of Aspect’s experiments are fascinating, but too long to go into here. For more detail on the experiments, see How to Teach Quantum Physics to Your Dog. The story behind the Clauser and Aspect experiments is also fascinating, and well told in David Kaiser’s How the Hippies Saved Physics.
11 George Musser’s book Spooky Action at a Distance is a good overview of the history of non-local interactions in physics, and exciting current research in the field.