Quantum entanglement with Freedman's inequality
Abstract
The assumption of local realism imposes constraints, such as Bell inequalities, on quantities obtained from measurements. In recent years, various tests of local realism have gained popularity in undergraduate laboratories, giving students the exciting opportunity to experimentally contradict this philosophical assumption. The standard test of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality requires 16 measurements, whereas a test of Freedman's inequality requires only three measurements. The calculations required to test Freedman's inequality are correspondingly simpler and the theory is less abstract. We suggest that students may benefit from testing Freedman's inequality before proceeding to the CHSH inequality and other more complicated experiments. Our measured data violated Freedman's inequality by more than six standard deviations.
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If a density matrix is separable, all eigenvalues of its partial transpose are non-negative; if the eigenvalues are negative, the density matrix is entangled.
“Therefore, if the density matrix ρˆ is separable, then, all eigenvalues of ρTA are non-negative. Otherwise, if the eigenvalues are negative; thus, ρˆ is entangled.”
From Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source (2021) · cites this paper as [82]
Logarithmic negativity is an upper bound to the distillable entanglement and is obtained from the Peres-Horodecki criterion for separability.
“Finally, the Logarithmic negativity, as upper bound to the distillable entanglement, which is obtained from the Peres-Horodecki criterion for separability [82], is defined as(22)EN(ρ)=log2trρˆ†TAρˆTA,”
From Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source (2021) · cites this paper as [82]
Cites
An introduction to QBism with an application to the locality of quantum mechanics
Fuchs, C. A., Mermin, N. D., & Schack, R. (2014) · American Journal of Physics · doi:10.1119/1.4874855 · Cited by 543 · see citing works
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Motazedifard, A., Madani, S. A., Dashkasan, J. J., & Vayaghan, N. S. (2021) · Heliyon · doi:10.1016/j.heliyon.2021.e07384 · Cited by 16 · see citing works
- Authors
- Brody, J., & Selton, C.
- Affiliations
- Emory University (US)
- ORCID
- Brody, Jed
- Venue
- American Journal of Physics
- Published
- 2018-06-01
- Volume
- 86
- Issue
- 6
- Pages
- 412-416
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W2803823862
- Cited by
- 7
- References
- 1
- Citations by year
- 2024: 3 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 1
- FWCI
- 0.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Social Sciences › Education › Science Education and Pedagogy
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- Bell inequalities, local realism, quantum entanglement, CHSH inequality, undergraduate laboratory experiment
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