Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits
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Quantum Physics arXiv:2601.12085 (quant-ph) [Submitted on 17 Jan 2026] Title:Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits Authors:Yu-Xuan Zhang, Jing-Ling Chen View a PDF of the paper titled Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits, by Yu-Xuan Zhang and Jing-Ling Chen View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2601.12085 [quant-ph] (or arXiv:2601.12085v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.12085 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jing-Ling Chen [view email] [v1] Sat, 17 Jan 2026 15:30:39 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits, by Yu-Xuan Zhang and Jing-Ling ChenView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)