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Chinese Physics B

Remote interactions on two distributed quantum systems: nonlocal unambiguous quantum-state discrimination

Libing Chen, Jin Rui-Bo, Haiping Lu

Published Mar 1, 2008• 3 citations
Publisher

Abstract

Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement (POVM). We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.

DOI
10.1088/1674-1056/17/3/007

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Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement (POVM). We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.
A set of linearly independent nonorthogonal symmetric d -level quantum states can be discriminated remotely and unambiguously with the aid of two-level Einstein–Podolsky–Rosen (EPR) states. We present a scheme for such a kind of remote unambiguous quantum state discrimination (UD). The probability of discrimination is in agreement with the optimal probability for local unambiguous discrimination among d symmetric states (Chefles and Barnettt 1998 Phys. Lett. A 250 223). This scheme consists of a remote generalized measurement described by a positive operator valued measurement (POVM). This remote POVM can be realized by performing a nonlocal 2 d × 2 d unitary operation on two spatially separated systems, one is the qudit which is encoded by one of the d symmetric nonorthogonal states to be distinguished and the other is an ancillary qubit, and a conventional local von Neumann orthogonal measurement on the ancilla. By decomposing the evolution process from the initial state to the final state, we construct a quantum network for realizing the remote POVM with a set of two-level nonlocal controlled-rotation gates, and thus provide a feasible physical means to realize the remote UD. A two-level nonlocal controlled-rotation gate can be implemented by using a two-level EPR pair in addition to local operations and classical communications (LOCCs).
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.
We propose a ``programmable'' quantum device that is able to perform a specific generalized measurement from a certain set of measurements depending on a quantum state of a ``program register.'' In particular, we study a situation when the programmable measurement device serves for the unambiguous discrimination between nonorthogonal states. The particular pair of states that can be unambiguously discriminated is specified by the state of a program qubit. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subsets it can be very close to the optimal value.
We consider one copy of a quantum system prepared with equal prior probability in one of two nonorthogonal entangled states of multipartite distributed among separated parties. We demonstrate that these two states can be optimally distinguished in the sense of conclusive discrimination by local operations and classical communications alone. This proves strictly the conjecture that Virmani et al. confirmed numerically and analytically. Generally the optimal protocol requires local POVM operations which are explicitly constructed. The result manifests that distinguishable information is obtained only and completely at the last operation and all prior operations give no information about that state.
The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. First, we introduce an efficiently computable quantity called the spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show that it can be a lower bound for the entanglement cost of optimal discrimination by PPT POVMs. Second, we establish an upper bound on the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging this result, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
Two pure orthogonal quantum states can be perfectly distinguished by sequential local action of multiple pairs of parties. However, this process typically leads to the complete dissolution of entanglement in the states being discriminated. We propose a protocol that allows an arbitrary number of pairs of parties to distinguish between any two orthogonal, entangled, two-qubit pure states using local quantum operations and classical communication, with a success probability greater than that of random guessing, while ensuring that at each step, the individual ensemble states retain a finite amount of entanglement. Our protocol employs the minimum-error state discrimination approach. For demonstrating the retention of entanglement in the ensemble states at each step, we use logarithmic negativity as well as the concept of entanglement witnessing. For a large family of sets of the two states, the success probability of discrimination can be as close as required to unity, while sustaining a finite amount of entanglement in each step.