Focus: Thwarting Post-Quantum Spies

Published June 30, 2005  |  Phys. Rev. Focus 15, 22 (2005)  |  DOI: 10.1103/PhysRevFocus.15.22

No Signaling and Quantum Key Distribution

Jonathan Barrett, Lucien Hardy, and Adrian Kent

Published June 27, 2005
Figure 1
Getty Images

Secret bits. Transmitting a binary number using the weirdness of quantum mechanics to detect eavesdroppers would work even if current quantum theory turns out to be incomplete, according to a new proof, as long as signals still can’t be sent faster than light.

If you want to keep a secret, all you have to do is believe. A new quantum mechanical recipe for encoding messages remains uncrackable even if the rules of quantum mechanics aren’t quite right–so long as it’s not possible to send messages faster than light. Reported in the 1 July PRL, the protocol lets secret-sharers foil “post-quantum” eavesdroppers essentially by pretending the rules of quantum mechanics still apply.

When sharing a coded message, the sender, Alice, generally uses binary numbers from a “key” to scramble the message, and the receiver, Bob, uses the key to decipher it. Of course, they must make sure Eve, the eavesdropper, does not get her hands on the key. Physicists have invented several schemes for secretly sharing a key by exchanging particles that obey the weird rules of quantum mechanics. The schemes allow Alice and Bob to tell if Eve is trying to read the key. Now Adrian Kent of the University of Cambridge in the UK and colleagues have devised a protocol that works even if quantum mechanics isn’t quite right.

The scheme exploits a spooky connection between particles called entanglement. Suppose Alice and Bob receive electrons from a common source. The electrons act like spinning tops, and each one headed toward Alice can be entangled with one headed toward Bob so that, if Alice finds her electron spinning up, Bob’s will also be spinning up. However, if Bob has tilted his measuring device so that “up” corresponds to 2 on a clock dial and “down” corresponds to 8, then the chances are 75 percent that Bob will find his pointing “up” and 25 percent that he will find it pointing “down,” according to the strange rules of quantum mechanics. Alice and Bob can use these statistical correlations to detect Eve.

The procedure goes like this: After twisting their devices at random and measuring many pairs, Alice and Bob talk on the phone and compare the orientations of their measuring devices for each pair of electrons. They then randomly pick some pairs for which their devices were nearly or perfectly aligned to make up the key. Alice and Bob do not reveal the results of their measurements for these pairs. Instead, they rely on entanglement to ensure that their measurements are the same. Interpreting ups and downs as 0s and 1s, they construct the shared key without ever uttering the digits in it.

To check for eavesdroppers, Alice and Bob do announce measurements for many other pairs. They compare these measurements and check the correlations against the predictions of quantum mechanics. Any discrepancies will tell them that Eve is snooping, because if she fiddles with the pairs in a way that will reveal the key, she will also mess up the correlations–at least according to quantum mechanics.

Curiously, the scheme works even if quantum mechanics isn’t exactly correct. Eve might, for example, try to tap into the key by entangling electrons of her own with the pairs. Quantum mechanics would prevent her from reading the key without detection, but Kent and colleagues suppose that she can manipulate particles in new ways using her understanding of a post-quantum theory. Those manipulations would produce different, non-quantum correlations among the triplets, which is essentially how the researchers define post-quantum theory.

However, Alice and Bob can still thwart Eve by sticking to the scheme and checking their correlations against standard predictions. To avoid detection, Eve must ensure that Alice and Bob see the correlations they’re expecting. But then she cannot read the key, the theorists prove mathematically. To do that, Eve would have to generate correlations that would allow Alice, Bob, and Eve to share messages faster than light–violating a basic premise of relativity theory.

“This is a beautiful result,” says Pawel Horodecki of the Technical University of Gdansk, in Poland. The work underlines the importance of the universal speed limit in quantum key distribution, Horodecki says: “It’s like pointing out with a finger which part of quantum mechanics is responsible for security on the most basic level.”

–Adrian Cho

Adrian Cho is a freelance science writer in Boone, NC.


Subject Areas

New in Physics