The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space.
Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixed-unitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixed-unitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels.
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 discrim…
We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). As standard completely positive trace preserving maps are known not to be appropriate to represent coherently controlled quantum channels, we propose to instead use purified channels, an extension of Stinespring's dilation. We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Rényi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Rényi relative entropy for the interval $α\in(0,1) $ of the Rényi parameter $α$. In …
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…
Monolithic Quantum Error Correction in the Presence of Distinguishability
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Center for Quantum Science and Engineering, Department of Physics & Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文学系量子科学与工程中心）；Department of Physics & Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文学系）；Joint Quantum Institute, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学联合量子研究所）
We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e., sources that emit one of two possible quantum states with given prior probabilities. Such a source can be represented by a classical-quantum state of a composite system $XA$, corresponding to an ensemble of two quantum states, with $X$ being classical and $A$ being quantum. We study the resource theory for two different classes of free operations: $(i)$ ${\rm{CPTP}}_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doub…
Adversarial Hypothesis Testing for Quantum Channels
School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；International Quantum Academy（国际量子学院）；Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）；Department of Electrical Engineering, the Graduate Institute of Communication Engineering, the Department of Mathematics, and the Institute of Applied Mathematical Sciences, and the Center for Quantum Science and Engineering, National Taiwan University（台湾大学电机工程学系、通信工程学研究所、数学学系、应用数学科学研究所及量子科学与工程中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）；Hon Hai (Foxconn) Quantum Computing Center（富士康（鸿海）量子计算中心）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；Wuhan Institute of Quantum Science and Technology（武汉量子技术研究院）
The framework of postselection is becoming more and more important in various recent directions in Quantum Computation research. Postselection renders simple computational models able to perform general quantum computation. This was first observed for the linear optics model [E. Knill, R. Laflamme, G. J. Milburn, Nature 409, 46 (2001)], and has since provided us with many near-term candidates for the quantum advantage, commuting computations [M. J. Bremner, R. Jozsa, D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)] being the first. To facilitate the discussion of errors in the presence of post…
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…
Quantum Channel Stein Theorem beyond Definite Causal Order
QudeLeap Research, Shanghai 200030, China（科跃研究）；Thrust of Artificial Intelligence, Information Hub,The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China（香港科技大学（广州）人工智能 thrust 信息枢纽）
Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
基于H.- P. Breuer等人，物理修订版信函\textbf{103}，210401（2009），即，通过量化从环境返回到开放系统的信息流。我们在这里用保真度代替迹距来评价量子态的可分辨性。我们使用我们的措施来评估两个范例高斯信道的非马尔可夫性：纯阻尼信道和量子布朗运动信道与欧姆环境。我们考虑不同类别的高斯状态，并寻找最大化信息回流的状态对。对于相干态，我们找到了简单的解析解，而对于压缩态，我们在弱耦合极限下提供了精确的数值解和近似的解析解。
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…
Amplitude damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the performance of such protocols. Since adaptivity has been shown to improve the performance of discrimination protocols, bounds on the distinguishability of AD channels must take this into account. In this paper, we use both channel simulation and a bound based on the diamond norm to significantly tighten the upper bound on the trace norm between the possible output…
