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Entanglement-Assisted Discrimination of Nonlocal Sets of Orthogonal States

Ziying Hou, Huaqi Zhou, Limin Gao

Abstract

Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with $n>3$) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.

Entanglement-Assisted Discrimination of Nonlocal Sets of Orthogonal States

Abstract

Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with ) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.
Paper Structure (18 sections, 10 theorems, 192 equations, 3 figures)

This paper contains 18 sections, 10 theorems, 192 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Local Discrimination of the GHZ Bases with Genuine Quantum Nonlocality
  4. Local Distinguishability of the GHZ Basis in a Four-Qubit System
  5. Local Distinguishability of the GHZ Basis in a Five-Qubit System
  6. Discrimination of Strongly Nonlocal OPSs in Four-Partite Systems
  7. Asymmetric Case
  8. Symmetric Case
  9. Discrimination of Symmetric Strongly Nonlocal OPSs in Five-Partite Systems
  10. Conclusion
  11. The proof of Theorem 3
  12. The proof of Theorem 4
  13. The proof of Theorem 5
  14. The proof of Theorem 6
  15. The proof of Theorem 7
  16. ...and 3 more sections

Key Result

Theorem 1

In a four-qubit system, the nonlocal basis given by Eq. (set3.1) can be perfectly discriminated using the entanglement resource configuration $(1,|\phi^{+}(2)\rangle_{AB})$.

Figures (3)

  • Figure 1: Circuit diagram of the discrimination scheme for the GHZ basis (\ref{['set3.1']}) in a four-qubit system. Lines $A$ and $a$ correspond to Alice's main subsystem and ancilla, respectively; lines $B$ and $b$ correspond to Bob's main subsystem and ancilla, respectively. The lower lines $C$ and $D$ correspond to Charlie and Dave. The meter denotes a measurement operation.
  • Figure 2: Circuit diagram of the discrimination scheme for the genuinely nonlocal set (\ref{['set3.2']}). Lines $A$ and $a$ correspond to Alice's main subsystem and ancilla, respectively; lines $B$ and $b$ correspond to Bob's main subsystem and ancilla, respectively. The lower lines $C$, $D$, and $E$ correspond to Charlie, Dave, and Eve. The meter denotes a measurement operation.
  • Figure 3: Comparison of total entanglement consumed by Theorem \ref{['thm:asym-ops-2']} and Theorem \ref{['thm:asym-ops-3']} for $d_1=4$ and $d_2=4$. The green plane $T_4$ and the gradient surface $T_5$ correspond to Theorem \ref{['thm:asym-ops-2']} and Theorem \ref{['thm:asym-ops-3']}, respectively.

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Theorem 8
  • ...and 2 more