Recently, the resource theory of asymmetric distinguishability for quantum strategies was introduced by [Wang et al., Phys. Rev. Research 1, 033169 (2019)]. The fundamental objects in the resource theory are pairs of quantum strategies, which are generalizations of quantum channels that provide a framework to describe an arbitrary quantum interaction. In the present paper, we provide semi-definite program characterizations of the one-shot operational quantities in this resource theory. We then apply these semi-definite programs to study the advantage conferred by adaptive strategies in discrimination and distinguishability distillation of generalized amplitude damping channels. We find that there are significant gaps between what can be accomplished with an adaptive strategy versus a non-adaptive strategy.
MESA+ Institute for Nanotechnology, University of Twente（特温特大学 MESA+ 纳米技术研究所）；Department of Applied Physics and Science Education, Eindhoven University of Technology（埃因霍温理工大学应用物理与科学教育部）；Department of Electrical Engineering, Eindhoven University of Technology（埃因霍温理工大学电气工程系）
The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the distinguishability of quantum channels. Characterizations of its unit ball and dual norm are established via strong duality of a semidefinite optimization problem. A full, formal proof of strong duality is presented for the semidefinite optimization problem in question. This norm and its properties are employed to generalize a state discrimination result of Ref. [GW05]. The …
Distinguishability of photons in non-operational degrees of freedom compromises unconditional security of quantum key distribution since an eavesdropper can improve attack strategies by exploiting this distinguishability. However, the optimal eavesdropping strategies in the presence of light source side channels are not known. Here we provide several explicit attack strategies on the BB84 protocol with partially distinguishable photons. In particular, we consider the phase-covariant cloning attack, which is optimal in the absence of side channels, and show that there are even better strategies…
We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific…
Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Indian Institute of Technology Bhubaneswar（印度技术学院布巴内斯瓦尔分校）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Indian Institute of Technology Bhubaneswar（布巴内斯瓦尔印度理工学院）；International Institute of Information Technology Hyderabad（海得拉巴国际信息技术学院）；Gdańsk University of Technology（格但斯克理工大学）；University of Gdańsk（格但斯克大学）
State-dependent cloning machines that have so far been considered either deterministically copy a set of states approximately, or probablistically copy them exactly. In considering the case of two equiprobable pure states, we derive the maximum global fidelity of $N$ approximate clones given $M$ initial exact copies, where $N>M$. We also consider strategies which interpolate between approximate and exact cloning. A tight inequality is obtained which expresses a trade-off between the global fidelity and success probability. This inequality is found to tend, in the limit as $N{\to}{\infty}$, to …
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions tha…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states of all N systems are different. We investigate the possibility of unambiguously obtaining this kind of information. It is found that some unambiguous comparison tasks are possible only when certain linear independence conditions are satisfied. We also obtain measurement strategies for certain comparison tasks which are optimal under a broad range of circumst…
Evaluating the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
University of Oulu（奥卢大学）；Indian Institute of Science（印度科学学院）；OP Financial Group（OP金融集团）
We assess the resources needed to identify a reversible quantum gate among a finite set of alternatives, including in our analysis both deterministic and probabilistic strategies. Among the probabilistic strategies we consider unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, and we prove that parallel strategies are sufficient to unambiguously identify the unknown gate with minimum number of queries. This result is used to provide upper and lower bounds on the query complexity and on the minimum ancilla dimension. In addition, we introduce …
Quantum Inspired Encoding Strategies for Machine Learning Models: Proposing and Evaluating Instance Level, Global Discrete, and Class Conditional Representations
It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi [IEEE Trans. Inf. Theory 55(8), 3807 (2009)] showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein's lemma for classical-quantum channels by showing that asymptotically the exponential error rate for classical-quantum cha…
