01608nas a2200145 4500008004100000245006400041210006400105260001400169520115800183100002201341700002401363700001801387700002001405856003701425 2021 eng d00aEstimating distinguishability measures on quantum computers0 aEstimating distinguishability measures on quantum computers c8/18/20213 a

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity, and we evaluate their performance using simulators of quantum computers. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate these algorithms by using a variational approach with parameterized quantum circuits and find that they converge well for the examples that we consider. 

1 aAgarwal, Rochisha1 aRethinasamy, Soorya1 aSharma, Kunal1 aWilde, Mark, M. uhttps://arxiv.org/abs/2108.0840601893nas a2200145 4500008004100000245006300041210006300104260001300167490000800180520147500188100001401663700002001677700001301697856003701710 2020 eng d00aEfficiently computable bounds for magic state distillation0 aEfficiently computable bounds for magic state distillation c3/6/20200 v1243 a

Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum "magic." In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation. 

1 aWang, Xin1 aWilde, Mark, M.1 aSu, Yuan uhttps://arxiv.org/abs/1812.1014506978nas a2200109 4500008004100000245009100041210006900132520659600201100001406797700002006811856003706831 2018 eng d00aExact entanglement cost of quantum states and channels under PPT-preserving operations0 aExact entanglement cost of quantum states and channels under PPT3 a

This paper establishes single-letter formulas for the exact entanglement cost of generating bipartite quantum states and simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the κ-entanglement of a quantum state. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum states. Notably, this is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception of entanglement theory over two decades ago. Next, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. The entanglement cost in both cases is given by the same single-letter formula and is equal to the largest κ-entanglement that can be shared by the sender and receiver of the channel. It is also efficiently computable by a semidefinite program. 

1 aWang, Xin1 aWilde, Mark, M. uhttps://arxiv.org/abs/1809.09592