Collectibility for mixed quantum states
Open accessAbstract
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.
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The setup applied in this work was also used earlier in Refs.48-51 for conceptually different tasks.
“We note that the setup applied in this work was also used earlier in Refs.48–51, but for conceptually different tasks, e.g., measuring collective nonlinear witnesses of entanglement52,53, Bell nonlocality measure54, or diagnosing an entanglement-swapping protocol.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [53]
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- Authors
- Rudnicki, Ł., Puchała, Z., Horodecki, P., & Życzkowski, K.
- Affiliations
- Center for Theoretical Physics (PL)
- Jagiellonian University (PL)
- Gdańsk University of Technology (PL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-12-26
- Volume
- 86
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2042618062
- Cited by
- 20
- References
- 35
- Citations by year
- 2025: 2 · 2024: 4 · 2023: 1 · 2022: 1 · 2021: 1 · 2020: 2 · 2018: 2 · 2017: 1 · 2016: 2 · 2015: 2 · 2014: 2
- FWCI
- 1.26
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Jagiellonian University Repository (Jagiellonian University) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- collectibility, entanglement detection, mixed quantum states, entropic uncertainty relations, positive partial transpose, multipartite entanglement, collective measurements, coincidence detection, two-qubit systems
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