Geometric block-coherence and quantum state discrimination

Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. From the perspective of operational meaning, geometric coherence can be equal to the minimum error probability to discriminate a set of pure states [J. Phys. A: Math. Theor. 51, 414005 (2018)]. By regarding coherence as a physical resource, Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] presented a comprehensive framework for coherence. Recently, geometric block-coherence as an effective block-coherence measure has been proposed. In this paper, we reveal an equivalence relationship between mixed quantum state discrimination task and geometric block-coherence, which provides an operational interpretation for geometric block-coherence and generalizes the main result in coherence resource theory. Meanwhile, we show that partial coherence is a special case of block-coherence. By linking the relationship between geometric partial coherence and quantum state discrimination tasks, we show that the value range of the two measures is the same. Finally, we reveal the relationship between geometric POVM-based coherence and quantum state discrimination task.

Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.

Protocol for unambiguous quantum state discrimination using quantum coherence

Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.

Support Vector Machines with Quantum State Discrimination

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.