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Communications in Theoretical Physics

Calculation of Entanglement Entropy for Continuous-Variable Entangled State Based on General Two-Mode Boson Exponential Quadratic Operator in Fock Space

Dai Fang-Wen, Лей Ма

Published Mar 1, 2008• 0 citations
Publisher

Abstract

We obtain an explicit formula to calculate the entanglement entropy of bipartite entangled state of general two-mode boson exponential quadratic operator with continuous variables in Fock space. The simplicity and generality of our formula are shown by some examples.
DOI
10.1088/0253-6102/49/3/14

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By virtue of the linear quantum transformation theory(LQTT), a general formula is obtained, which calculate the quantum fluctuations for bipartite entangled state of continuous variables in Fock space. Moreover, the squeezed properties of the entangled state are discussed. The relations between the state parameters are depicted by means of the linear fitting, when the degree of the fluctuation and entanglement entropy reach the extremum. When the entangled state is maximally entangled, the results show that the squeezed degree is also maximal. In addition, the changing relationship between the quantum fluctuations and the quantum entanglement is acquired. The derived formula are used to calculate the fluctuation of the common two-mode squeezed vacuum state and the two-mode one-sided squeezed vacuum state as examples.
Abstract In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues , elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.
We present an approach to the analysis of entanglement in smooth bipartite continuous-variable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some region of space; we study the entanglement remaining after filtering. For small regions, a two-mode system can be approximated by a pair of qubits and its entanglement fully characterized, even for mixed states. Our approach may be extended to any smooth bipartite pure state or two-mode mixed state, leading to natural definitions of concurrence and negativity densities. For Gaussian states both these quantities are constant throughout configuration space.