Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits

• URL: http://arxiv.org/abs/2601.12085v1
• Date: Sat, 17 Jan 2026 15:30:39 GMT
• Title: Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits
• Authors: Yu-Xuan Zhang, Jing-Ling Chen,
• Abstract summary: Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen steering.<n>We show that a Peres-type criterion can be established for EPR steering in the two-qubit system.<n>We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state.
• Score: 5.478582839093083
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.

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