On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock... In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form $$(|N-m\rangle _a|m\rangle _b+\mathrm{e}^{i (N-2m)\phi }|m\rangle _a|N-m\rangle _b)/\sqrt{2}$$ ( | N - m ⟩ a | m ⟩ b + e i ( N - 2 m ) ϕ | m ⟩ a | N - m ⟩ b ) / 2 have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state $$(|N\rangle _a|0\rangle _b+\mathrm{e}^{i N\phi }|0\rangle _a|N\rangle _b)/\sqrt{2}$$ ( | N ⟩ a | 0 ⟩ b + e i N ϕ | 0 ⟩ a | N ⟩ b ) / 2 and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

, Volume 15 (3) – Aug 12, 2015
18 pages

/lp/springer_journal/on-the-connection-between-quantum-nonlocality-and-phase-sensitivity-of-yKgZjm0Kb1
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1082-1
Publisher site
See Article on Publisher Site

Abstract

In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form $$(|N-m\rangle _a|m\rangle _b+\mathrm{e}^{i (N-2m)\phi }|m\rangle _a|N-m\rangle _b)/\sqrt{2}$$ ( | N - m ⟩ a | m ⟩ b + e i ( N - 2 m ) ϕ | m ⟩ a | N - m ⟩ b ) / 2 have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state $$(|N\rangle _a|0\rangle _b+\mathrm{e}^{i N\phi }|0\rangle _a|N\rangle _b)/\sqrt{2}$$ ( | N ⟩ a | 0 ⟩ b + e i N ϕ | 0 ⟩ a | N ⟩ b ) / 2 and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 12, 2015

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