Chinese Physics B

General description of discriminating quantum operations

Kejia Zhang, Ping Zhu, Fei Gao, Fen-Zhuo Guo, Su‐Juan Qin, Qiaoyan Wen

Published Oct 1, 2011• 2 citations

Abstract

The discrimination of quantum operations plays a key role in quantum information and computation. Unlike discriminating quantum states, it has some special properties which can be carried out in practice. In this paper, we provide a general description of discriminating quantum operations. Concretely speaking, we describe the distinguishability between quantum operations using a measure called operator fidelity. It is shown that, employing the theory of operator fidelity, we can not only verify some previous results to discriminate unitary operations, but also exhibit a more general discrimination condition. We further apply our results to analysing the security of some quantum cryptographic protocols and discuss the realization of our method using well-developed quantum algorithms.

DOI: 10.1088/1674-1056/20/10/100304

Related papers

Unambiguous discrimination of general quantum operations

Weizhou Cai, Jing-Ning Zhang, Ziyue Hua +10 more

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research notably advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related to the discrimination of quantum states, and proof-of-principle demonstrations of the latter have already been realized using optical photons. However, the experimental demonstration of discriminating general quantum operations, including both unitary and nonunitary operations, has remained elusive. In general quantum systems, especially those with high dimensions, the preparation of arbitrary quantum states and the implementation of arbitrary quantum operations and generalized measurements are nontrivial tasks. Here, we experimentally demonstrate the optimal unambiguous discrimination of up to six displacement operators and the unambiguous discrimination of nonunitary quantum operations. Our results demonstrate powerful tools for experimental research in quantum information processing and are expected to stimulate a wide range of valuable applications in the field of quantum sensing.

arXiv:2404.13317Science AdvancesNov 13, 20243 citations

Derivation of standard quantum theory via state discrimination

Hayato Arai, Masahito Hayashi

Abstract It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of general probabilistic theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality, are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.

arXiv:2307.11271New Journal of PhysicsMay 1, 20243 citations

Discrimination of two-qubit unitaries via local operations and classical communication

Joonwoo Bae

Distinguishability is a fundamental and operational measure generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and also characterises capabilities of related information tasks. In this work, we consider discrimination between bipartite two-qubit unitary transformations by local operations and classical communication (LOCC) and its relations to entangling capabilities of given unitaries. We show that a pair of entangling unitaries which do not contain local parts, if they are perfectly distinguishable by global operations, can also be perfectly distinguishable by LOCC. There also exist non-entangling unitaries, e.g. local unitaries, that are perfectly discriminated by global operations but not by LOCC. The results show that capabilities of LOCC are strictly restricted than global operations in distinguishing bipartite unitaries for a finite number of repetitions, contrast to discrimination of a pair of bipartite states and also to asymptotic discrimination of unitaries.

arXiv:1601.07256Scientific ReportsDec 15, 201515 citations

Optimal Perfect Distinguishability between Unitaries and Quantum Operations

Cheng Zhu Lu, Jianxin Chen, Runyao Duan

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations.

arXiv:1010.2298Oct 12, 20103 citations

Optimal discrimination between quantum operations

Lvzhou Li, Daowen Qiu

In this paper, we address the problem of discriminating two given quantum operations. Firstly, based on the Bloch representation of single qubit systems, we give the exact minimum error probability of discriminating two single qubit quantum operations by unentangled input states. In particular, for the Pauli channels discussed in [Phys. Rev. A {\bf 71}, 062340 (2005)], we use a more intuitional and visual method to deal with their discrimination problem. Secondly, we consider the condition for perfect discrimination of two quantum operations. Specially, we get that two generalized Pauli channels are perfectly distinguishable if and only if their characteristic vectors are orthogonal.

arXiv:0705.2549Journal of Physics A Mathematical and TheoreticalJul 11, 200813 citations

Higher-order quantum computation for equivalence determination of unitary operations

厚新保

Quantum state discrimination is one of the most fundamental tasks in quantum information since it describes the read-out process of classical information from quantum states in quantum communications.In quantum state discrimination, a given test state is guaranteed to be identical to one of a set of candidate quantum states.The task is to determine the identity of the test state by performing an appropriate quantum measurement based on the classical descriptions of the candidate states.Quantum state discrimination also has several connections to the principles of quantum mechanics such as the no-cloning theorem and the no-signaling principle.One of fundamental properties of quantum mechanics is that the exact classical description of unknown quantum states cannot be retrieved from a single copy of the physical state.Quantum state discrimination in the case that the candidate states are given as two unknown physical states (reference states) but their classical descriptions are not given, has been investigated.The two reference states are labeled one and two, respectively.The task is to determine which of the two reference states is equivalent to the test state, whereas the descriptions of the states are not of interest.We call such a task as equivalence determination of quantum states.Discrimination of quantum operations has been also investigated and it has been shown that there is an intrinsic difference between discrimination of quantum state and discrimination of quantum operations.We analyze a unitary operation version of the equivalence determination task by using the concept of higher-order quantum computation to investigate properties of discrimination of other quantum objects.We consider three black-boxes (test box and reference boxes) implementing unknown unitary operations given as physical systems.The test box is guaranteed to implement one of the two unitary operations given by the reference boxes.Equivalence determination of unitary operations is a task to determine the reference box implementing the same unitary operation as the one by the test box.We assume that the unitary operations of the reference boxes are randomly sampled from the Haar measure of SU(2).We first consider the case that each of three black-boxes can be used only once both in parallel and ordered uses of the black-boxes.We show that the optimal success probability for equivalence determination is 7/8 by obtaining analytical solutions of the corresponding semidefinite programmings (SDPs) both in the parallel and ordered strategies.The optimal success probability can be achieved even without using one of the reference boxes.We also showed that entanglement of an initial state across the systems on which the reference boxes act and the test box acts is necessary to achieve the optimal success probability.We then consider the case that the multiple uses of the reference boxes are allowed.We consider the parallel strategies up to four uses of each of the reference boxes and obtain the optimal success probabilities by numerically solving the semidefinite programmings.We numerically show that the ordered strategies give improvement over the parallel strategies and the optimal success probability varies depending on the order of the black-boxes when one reference box is used once and the other reference box is used twice.This result indicates that an appropriate order of the black-boxes under the ordered strategies is necessary to obtain improvement over the parallel strategies. Chapter 1 Introduction Notations• H i , K j : Hilbert spaces labeled with i and j.• L(H): The set of linear operators on H.• L(H, K): The set of linear operators from H to K.• S(H) : The set of positive semidefinite linear operation of unit trace on H • Tr H : The partial trace over H • U † : The conjugate transpose of U • {Π i }: The positive operator-valued measure • { Π i }: The quantum tester • δ ij : The Kronecker delta, equal to 1 if i = j and 0 otherwise • dµ(•) : The Haar measure, the uniform distribution of the space of unitary operations • |I⟩⟩ : Unnormalized maximally entangled vector defined as |I⟩⟩ = i |i⟩|i⟩ • M : A quantum channel • M : Choi operator of a quantum channel M• U j : The irreducible subspace of the total angular momentum j.

Mar 22, 20180 citations