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Quantum state discrimination (QSD) in non-Hermitian systems is explored, showing unambiguous discrimination is possible even with complex spectra. Non-orthogonal eigenstates, not just symmetry, are key for information flow in these systems.

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Area of Science:

  • Quantum Information Processing
  • Non-Hermitian Physics
  • Quantum State Discrimination

Background:

  • Quantum state discrimination (QSD) is a fundamental problem in quantum information processing.
  • Existing research on QSD in non-Hermitian (NH) systems primarily focuses on PT-symmetric or pseudo-Hermitian systems with real spectra.
  • Generic NH Hamiltonians, however, possess complex spectra, necessitating further investigation.

Purpose of the Study:

  • To explore the underlying physics of quantum state discrimination (QSD) in generic non-Hermitian (NH) systems.
  • To demonstrate the feasibility of unambiguous discrimination of non-orthogonal quantum states in NH systems.
  • To establish criteria for constructing NH Hamiltonians that optimize QSD.

Main Methods:

  • Demonstration of unambiguous discrimination using P-pseudo-Hermitian and PT-symmetric Hamiltonians in the broken phase.
  • Extension of QSD feasibility to generic non-Hermitian Hamiltonians.
  • Establishment of criteria for P-pseudo-Hermitian Hamiltonians enabling enhanced QSD under energy constraints.

Main Results:

  • Unambiguous discrimination of non-orthogonal quantum states is achievable with P-pseudo-Hermitian and PT-symmetric Hamiltonians, with potentially arbitrarily small evolution times.
  • The feasibility of unambiguous discrimination is extended to generic non-Hermitian Hamiltonians.
  • P-pseudo-Hermitian Hamiltonians can be constructed to achieve unambiguous discrimination with smaller angular separation or shorter evolution times compared to fixed PT-symmetric systems.

Conclusions:

  • Non-orthogonal eigenstates of non-Hermitian Hamiltonians are fundamental to unambiguous discrimination and information flow.
  • PT symmetry or pseudo-Hermitian symmetry are not the sole determinants for QSD in NH systems.
  • The study expands the understanding of QSD in the broader context of non-Hermitian physics, highlighting the role of eigenstates.