Entangled photon-added coherent states We study the degree of entanglement of arbitrary superpositions of m, n photon-added coherent states (PACS) $$\mathinner {|{\psi }\rangle } \propto u \mathinner {|{{\alpha },m}\rangle }\mathinner {|{{\beta },n }\rangle }+ v \mathinner {|{{\beta },n}\rangle }\mathinner {|{{\alpha },m}\rangle }$$ | ψ ⟩ ∝ u | α , m ⟩ | β , n ⟩ + v | β , n ⟩ | α , m ⟩ using the concurrence and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: $$\mathinner {|{\psi }\rangle } \propto \mathinner {|{\alpha }\rangle }_a\mathinner {|{-\alpha }\rangle }_b + \mathinner {|{-\alpha }\rangle }_a\mathinner {|{\alpha }\rangle }_b$$ | ψ ⟩ ∝ | α ⟩ a | - α ⟩ b + | - α ⟩ a | α ⟩ b whose entanglement tends to zero for $$\alpha \rightarrow 0$$ α → 0 , can be maximal if al least one photon is added in a subsystem. A full family of maximally entangled PACS is also presented. We also analyzed the decoherence effects in the entangled PACS induced by a simple depolarizing channel . We find that robustness against depolarization is increased by adding photons to the coherent states of the superposition. We obtain the dependence of the critical depolarization $$p_{\text {crit}}$$ p crit for null entanglement as a function of $$m,n, \alpha$$ m , n , α and $$\beta$$ β . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

, Volume 15 (8) – May 5, 2016
16 pages

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/s11128-016-1325-9
Publisher site
See Article on Publisher Site

### Abstract

We study the degree of entanglement of arbitrary superpositions of m, n photon-added coherent states (PACS) $$\mathinner {|{\psi }\rangle } \propto u \mathinner {|{{\alpha },m}\rangle }\mathinner {|{{\beta },n }\rangle }+ v \mathinner {|{{\beta },n}\rangle }\mathinner {|{{\alpha },m}\rangle }$$ | ψ ⟩ ∝ u | α , m ⟩ | β , n ⟩ + v | β , n ⟩ | α , m ⟩ using the concurrence and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: $$\mathinner {|{\psi }\rangle } \propto \mathinner {|{\alpha }\rangle }_a\mathinner {|{-\alpha }\rangle }_b + \mathinner {|{-\alpha }\rangle }_a\mathinner {|{\alpha }\rangle }_b$$ | ψ ⟩ ∝ | α ⟩ a | - α ⟩ b + | - α ⟩ a | α ⟩ b whose entanglement tends to zero for $$\alpha \rightarrow 0$$ α → 0 , can be maximal if al least one photon is added in a subsystem. A full family of maximally entangled PACS is also presented. We also analyzed the decoherence effects in the entangled PACS induced by a simple depolarizing channel . We find that robustness against depolarization is increased by adding photons to the coherent states of the superposition. We obtain the dependence of the critical depolarization $$p_{\text {crit}}$$ p crit for null entanglement as a function of $$m,n, \alpha$$ m , n , α and $$\beta$$ β .

### Journal

Quantum Information ProcessingSpringer Journals

Published: May 5, 2016

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