Quantum state separation, unambiguous discrimination and exact cloning

We propose and prove a theoretical scheme of realizing programmable and controlled remote quantum-state unambiguous discrimination (UD) based on nonlocal system–ancilla unitary evolution. By decomposing the evolution process from the initial state to the final state, we first construct the required nonlocal unitary evolution, which is a nonlocal conditional rotation. Utilizing the entanglement property of Greenberger–Horne–Zeilinger (GHZ) class state, we then design a quantum network for implementing the controlled nonlocal conditional rotation gate, and thus provide a feasible physical means to realize the remote UD. The features of the scheme is that the particular pair of states of system (data register) that can be remotely and unambiguously discriminated is specified by the state of the ancilla (program register). Furthermore, a third side is included, who may participate the process of quantum remote implementation as a supervisor. When the quantum channel is partially entangled, the third one can rectify the state distorted by the imperfect quantum channel. The success probability of implementing this remote UD is also investigated.

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

Scientific Reports ◽

10.1038/s41598-021-97103-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Donghoon Ha ◽

Jeong San Kim

Keyword(s):

Quantum State ◽

Quantum States ◽

Quantum Nonlocality ◽

Quantum State Discrimination ◽

Classical Communication ◽

Minimum Error ◽

Prior Probabilities ◽

Separable States ◽

Unambiguous Discrimination ◽

State Discrimination

AbstractNonlocality 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.

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

Entropy ◽

10.3390/e22121422 ◽

2020 ◽

Vol 22 (12) ◽

pp. 1422

Author(s):

Min Namkung ◽

Younghun Kwon

Keyword(s):

Quantum Information ◽

Quantum State ◽

Quantum Key Distribution ◽

Key Distribution ◽

Quantum States ◽

Quantum State Discrimination ◽

Mixed States ◽

Generalized Measurement ◽

Unambiguous Discrimination ◽

State Discrimination

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.

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