The 1962 James bond movie 'Dr. No' taught children around the world a valuable lesson in how to detect whether nosy siblings are snooping into their rooms. You stick a small piece hair across the door and the doorframe. When the door is opened, the hair falls to the floor. The unsuspecting perpetrator has unwittingly communicated to you their rather unscrupulous action. The Bond hair trick demonstrates the power of knowledge; by knowing how a system is initially configured (the location of hair), one can gain information about actions that have affected the system (opening the door).
Indeed the one-time pad, a key method of secure communication, is based on this principle. Suppose Alice wishes to communicate a secret message to Bob sometime in the future. To do this, Alice and Bob gather in some secure location, where Alice generates a string of random bits that Bob commits to memory. Should Alice choose to flip some of these bits and give the resulting string to Bob, Bob is able to discern exactly which bits have been flipped by comparing the resulting string with the one stored in his memory. In contrast, anyone without access to Bob's memory would gain no information about Alice's actions. Exclusive knowledge about an ancillary system has again led to exclusive knowledge of how the system was manipulated.
In these scenarios, everything is classical. What happens in 2262, when Bond has quantized the hair?
When we think of classical knowledge, we envision information that can be represented on a piece of paper. To find out how a system has changed, Bob merely compares the new state of the system with what he has written down. In the one-time pad, for example, he can tell exactly which bits Alice flipped by isolating the bits that differ from what he has remembered. James bond's hair trick is no different; Bob can record on a piece of paper the exact location of his hair, and can discern whether the door has been opened by checking the hair has moved.
However, what if Bob can manipulate quantum information? Can Bob gain additional information about how a system is manipulated, by comparing his memory with the system `quantum mechanically'? Since this additional information cannot be accessed through classical means, we may consider it to be genuinely quantum.
The motivation for this is more fundamental than finding more efficient ways of incriminating a kid brother. Any knowledge' that can only be accessible by quantum computing is by definition, a resource that only quantum computer can take advantage of. Thus, isolation of this resource could help us answer a question that has fascinated the scientific community for the last decade.
What is the resource that allows quantum computers to do better than their classical counterparts?
Ironically, this was a question many scientists thought already answered a mere decade ago, it was of course, entanglement. After all, the main curiosity of quantum mechanics was that two objects could be so correlated that it was impossible to assign each system its own local reality, and this concept of non-classical correlations was entirely captured by entanglement. What else could there be?
Yet, this all changed in 2006, when it was discovered that DQC1, a protocol for computing the trace of a unitary matrix exponentially faster any known classical algorithm, featured negligible entanglement. The idea that entanglement wasn't the end all resource for quantum processing took off and the search for more general quantifiers of a quantum resource begun.
One potential candidate was quantum discord (*). Independently proposed by Vedral and Zurek as a measure of quantum correlations in the early 2000s, quantum discord had lived in obscurity for a good half decade. Yet, when discord was discovered in DQC1 in 2008, it was propelled into the center of scientific spotlight. Could discord be the resource that catalyzed the speed-up for quantum processing? Despite this excitement, speculation remained speculation. No formal links between discord and DQC1 was found. When Acin showed that a state picked at random would have discord in 2010, many wondered if the presence of discord in DQC1 was not merely a rather unsurprising coincidence.
In Nature Physics this week, we aimed to connect discord with `quantum knowledge', and in doing so, confirm that discord indeed quantifies a resource that bestows quantum processors the power to supersede their classical counterparts.
Our approach centered on memory that is unavoidably disturbed the second it is measured. In classical scenarios, this is a non-issue. If Bob's memory is stored on paper, it stays the same no matter how many times Bob looks at it. In quantum systems, this is no longer true. Two quantum states may be non-orthogonal such that one of the states will be disturbed regardless of your choice of measurement basis. Thus, should Bob's memory involve non-orthogonal states, Bob's very act of reading information from his memory will induce disturbance, and thus degrade its accuracy.
If Bob was however, armed with a quantum processor, some of this loss can be mitigated. There exist methods in which Bob can compare two systems quantum mechanically through the use of quantum interference, so that the disturbance due to measurement is minimized. Thus, Bob can deduce more information about how a system has been manipulated, by coherently interacting it with his memory.
The key feature is that non-orthogonality of Bob's memory guaranteed that Bob's memory and the system he cares about must contain quantum discord, but not necessarily quantum entanglement. In fact, we can prove that provided the system Bob is trying to track was manipulated is a sufficiently diverse manner, the boost in performance though quantum processing is given exactly by the discord.
We set to demonstrate this effect in realistic conditions via two optical beams. One acts as the system Bob wished to track (call this A), the other as Bob's memory of this system (call this B). The system and memory were then injected with enough correlations to generate discord, but not entanglement.
Then, like the scenario with James Bond, a perpetuator would take beam A, and manipulate it by giving it a random `kick' in both momentum and position. Bob takes the resulting beam, and is tasked to harness his memory to make the best possible guess on the magnitude of the perpetuator's kick.
In the experiment, we took on the role of Bob, and attempted to extract as much information about what the perpetrator did though quantum interference of Bob's memory, and the kicked beam. The amount of information we extracted beyond classical limits was shown to be indeed related to the amount of discord originally injected between A and B.
The experimental verification that discord quantifies exactly `quantum knowledge' that can be harnessed only be quantum processors has applications beyond philosophical interest. It could also pave the way for practical protocol to test whether an untrusted party has a quantum computer.
Suppose a salesman of the future knocks on your door with some alien device he claims to be a quantum computer. How can you ascertain that you're not being scammed? There are of course many ways to do this, such as, for example, challenging the salesman to distinguish between two different entangled states (such as Bell states). Such conventional tests, however, require you to be able to entangle states, which would require some quantum processor like the one the salesman's trying to sell you.
The inability for classical processors to harness discord suggest a simpler method. You get two quantum systems that share discord, and manipulate one of them in secret, and challenge the salesman to guess what you did. Since some of this information is completely inaccessible without interacting the systems quantum mechanically, any salesman who fails the test can get a swift kick out the door. Here the benefit of discord really shines. Discordant states are almost everywhere, and thus much easier to prepare than entangled states. Unlike entanglement, you never need to interact the two systems quantum mechanically.
Of course, many questions still remain unanswered. While our protocol has confirmed that quantum processors can harness discordant correlations to better deduce how other systems have being manipulated, there's still no direct link to computational power. Could we think about some forms of computation, such as computing the trace of a matrix in DQC1, as just trying to form the best guess of which unknown unitary matrix was applied to a system we have prior knowledge of? If so, then knowledge is indeed the power, the more you can know, the faster you can compute.
(In the image above, Helen Chrzanowski sets up to demonstrate the unique power of quantum processors in harnessing discord at the Australian National University.)
Note (*): Discord between two systems, A and B are defined as the difference between two quantum variants of their mutual information, I and J. Where I = S(A) + S(B) - S(A,B), and J = S(A) - S(A|B_Pi). Here S(A) and S(B) denote the entropy of system A and system B, while S(A,B) is the joint entropy of A and B and S(A|B_Pi) is the entropy of A after measurement of B is basis Pi, minimized over all possible measurements.聽