Speakers Rui Chao, Andrea W. Coladangelo, Matthew Coudron

Опубликовано 3 февраля 2017, 19:29

1. Overlapping qubits 2. Parallel self-testing of (tilted) EPR pairs via copies of (tilted) CHSH 3. The parallel-repeated magic square game is rigid

"1. An ideal system of n qubits has 2^n dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can ""overlap,"" in the sense that an operation on one qubit slightly affects the others.

We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be <= epsilon in n^{O(1/epsilon^2)} dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power.

On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices. 2. Device-independent self-testing allows a verifier to certify that potentially malicious parties hold on to a specific quantum state, based only on the observed correlations. Parallel self-testing has recently been explored, aiming to self-test many copies (i.e. a tensor product) of the target state concurrently. In this work, we show that n EPR pairs can be self-tested in parallel through n copies of the well known CHSH game. We generalise this result further to a parallel self-test of n tilted EPR pairs with arbitrary angles, and finally we show how our results and calculations can also be applied to obtain a parallel self-test of 2n EPR pairs via n copies of the Mermin-Peres magic square game. 3. We show that the n-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability 1 - \epsilon, the players' shared state is O(poly(n \epsilon))-close to 2n EPR pairs under a local isometry. Furthermore, we show that, under local isometry, the players' measurements in said entangled strategy must be O(poly(n \epsilon))-close to the ""ideal"" strategy when acting on the shared state."