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General Method for Constructing Local Hidden Variable Models for Entangled Quantum States.

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This study introduces a general test to identify local quantum states, crucial for understanding entanglement and nonlocality in quantum information. The method, implementable via semidefinite programming, helps distinguish between entangled and local states.

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Area of Science:

  • Quantum Information Theory
  • Quantum Foundations
  • Quantum Computing

Background:

  • Entanglement is a key resource for quantum information protocols, enabling nonlocality.
  • Not all entangled quantum states exhibit nonlocality, necessitating a clear distinction.
  • Understanding the relationship between entanglement and nonlocality is central to quantum theory.

Purpose of the Study:

  • To develop a general test for determining if a quantum state is local.
  • To provide a method for constructing new examples of states with local hidden variable models.
  • To estimate the fraction of local entangled states in two-qubit systems.

Main Methods:

  • Development of a general test for quantum state locality.
  • Implementation of the test using semidefinite programming.
  • Application to various quantum states, including noisy and Bell-diagonal states.

Main Results:

  • The first general test for quantum state locality is presented.
  • The test is shown to be implementable via semidefinite programming.
  • New examples of local states and lower bounds for local entangled states are provided.

Conclusions:

  • A robust method for distinguishing local from nonlocal quantum states is established.
  • Semidefinite programming offers a practical approach to analyze quantum state locality.
  • The findings contribute to a deeper understanding of entanglement and nonlocality in quantum mechanics.