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Entanglement degradation of a two-mode squeezed vacuum in absorbing and amplifying optical fibers

Scheel, S, Opatrny, T, Welsch, D G

Published Jun 6, 2000• 1 citation
OpenAlex

Abstract

Applying the recently developed formalism of quantum-state transformation of light at absorbing dielectric four-port devices [5], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres-Horodecki separability criterion for continuous variable systems [4], we then compute both the maximal length of transmission of a two-mode squeezed vacuum through an absorbing system for which the transmitted state is still inseparable and the maximal gain for which inseparability can be observed in an amplifying setup. Finally, we estimate an upper bound of the entanglement preserved after transmission through an absorbing system. The results show that the characteristic length of entanglement degradation drastically decreases with increasing strength of squeezing.

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Chinese Physics Letters•Aug 4, 2004•11 citations
Applying the recently developed formalism of quantum-state transformation of light at absorbing dielectric four-port devices [5], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres-Horodecki separability criterion for continuous variable systems [4], we then compute both the maximal length of transmission of a two-mode squeezed vacuum through an absorbing system for which the transmitted state is still inseparable and the maximal gain for which inseparability can be observed in an amplifying setup. Finally, we estimate an upper bound of the entanglement preserved after transmission through an absorbing system. The results show that the characteristic length of entanglement degradation drastically decreases with increasing strength of squeezing.
Applying the recently developed formalism of quantum-state transformation of light at absorbing dielectric four-port devices [5], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres-Horodecki separability criterion for continuous variable systems [4], we then compute both the maximal length of transmission of a two-mode squeezed vacuum through an absorbing system for which the transmitted state is still inseparable and the maximal gain for which inseparability can be observed in an amplifying setup. Finally, we estimate an upper bound of the entanglement preserved after transmission through an absorbing system. The results show that the characteristic length of entanglement degradation drastically decreases with increasing strength of squeezing.
The influence of losses in the transmission of continuous-variable entangled light through linear devices such as optical fibers is studied, with special emphasis on Gaussian states. Upper bounds on entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement and thus do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure. In particular, it shows that losses give rise to entanglement saturation, which principally limits the amount of information that can be transferred quantum mechanically in continuous-variable teleportation. Even for an initially infinitely squeezed two-mode squeezed vacuum, high-fidelity teleportation is only possible over distances that are much smaller than the absorption lengths.
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure.
The problem of decorrelation of entangled (squeezed-vacuum-type) light pulses of arbitrary shape passing through dispersive and absorbing four-port devices of arbitrary frequency response is studied, applying recently obtained results on quantum-state transformation (L Knöll et al 1999 Phys. Rev. A 59 4716). The fidelity and indices of (quantum) correlation based on the von Neumann entropy are calculated, with special emphasis on the dependence on the mean photon number, the pulse shape and the frequency response of the devices. In particular, it is shown that the quantum correlations can decay very rapidly due to dispersion and absorption, and the degree of degradation intensifies with increasing mean photon number.
By numerically analysing the entropy of entanglement of the output state from a Mach–Zehnder interferometer for the two-mode squeezed vacuum state input, it is found that if the internal phase shift of the interferometer is adjusted to the value of 0 or π, the entangling characteristic of the input state is efficiently preserved at the output. If the internal phase shift is tuned to the value of π/2, the two-mode squeezed vacuum state is completely disentangled at the output of the setup. If the internal phase shift deviates from the above values, the input state is degraded into a partially entangled output state. Based on these results, a method for optically realizing the entanglement preservation, entanglement degradation, and disentanglement via the interferometer is obtained.