https://doi.org/10.1140/epjd/s10053-022-00559-4
Regular Article – Quantum Optics
Covariance-based separability criterion for the output state of a SU(2) system
Extreme Light Infrastructure - Nuclear Physics (ELI-NP), “Horia Hulubei” National R &D Institute for Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului Street, 077125, Bucharest-Măgurele, Romania
Received:
14
June
2022
Accepted:
14
November
2022
Published online:
3
December
2022
Determining if a quantum state is separable or entangled is a complex problem. Proposed schemes usually employ the von Neumann entropy, the positivity of the partial transpose or various inequalities. Determining the separability of the output of an optical system is an even more involved task. In this paper, we find necessary conditions for the output separability of a SU(2) system. We first discuss some previously reported criteria, showing their limitations. We then introduce our covariance-based criterion and assess its performance. For a system having one input port in the vacuum state, we arrive at a very simple criterion for the output separability. For pure input states, we introduce an artifice to easily assess the output separability with the help of the two-parameter quantum Fisher information. Applications of the proposed criterion are given by evaluating the output separability of a non-balanced beam splitter, fed by a number of input states.
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