Title:	Lorentzian geometry for detecting qubit entanglement
Authors:	Samuel, J. Shivam, Kumar Sinha, Supurna
Keywords:	Quantum entanglement Qubits Lorentzian geometry Relativity and energy conditions
Issue Date:	Sep-2018
Publisher:	Elsevier Inc.
Citation:	Annals of Physics, 2018, Vol.396, p159-172
Abstract:	We describe a new approach based on Lorentzian geometry to detect qubit entanglement. The treatment is based physically, on the causal structure of Minkowski spacetime, and mathematically, on a Lorentzian Singular Value Decomposition. A surprising feature is the natural emergence of “Energy conditions” used in Relativity. All states satisfy a “Dominant Energy Condition” (DEC) and separable states satisfy the Strong Energy Condition(SEC), while entangled states violate the SEC. We thus propose a test for two qubit entanglement which is an alternative to the positive partial transpose (PPT) test. This test is based on the partial Lorentz transformation (PLT) on individual qubits. Apart from testing for entanglement, our approach also enables us to construct a separable form for the density matrix in those cases where it exists. Our approach leads to a simple graphical three dimensional representation of the state space which shows the entangled states within the set of all states.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/6983
ISSN:	0003-4916
Alternative Location:	https://arxiv.org/abs/1801.00611 https://doi.org/10.1016/j.aop.2018.07.019 http://adsabs.harvard.edu/abs/2018AnPhy.396..159S
Copyright:	2018 Elsevier Inc.
Appears in Collections:	Research Papers (TP)

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