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Laser Physics Letters

Laguerre-polynomial-weighted squeezed vacuum: generation and its properties of entanglement

Wei Ye, Kuizheng Zhang, Haoliang Zhang, Xue-xiang Xu, Liyun Hu

Published Jan 16, 2018• 11 citations
Publisher

Abstract

Abstract We theoretically prepare a kind of two-mode entangled non-Gaussian state generated by combining quantum catalysis and parametric-down amplifier operated on the two-mode squeezing vacuum state. We then investigate the entanglement properties by examining Von Neumann entropy, EPR correlation, squeezing effect and the fidelity of teleportation. It is shown that only Von Neumann entropy can be enhanced by both single- and two-mode catalysis in a small squeezing region, while the other properties can be enhanced only by two-mode catalysis including symmetrical and asymmetrical cases. A comparison among these properties shows that the squeezing and the EPR correlation definitely lead to the improvement of both the entanglement and the fidelity, and the region of enhanced fidelity can be seen as a sub-region of the enhanced entanglement which indicates that the entanglement is not always beneficial for the fidelity. In addition, the effect of photon-loss after catalysis on the fidelity is considered and the symmetrical two-photon catalysis may present better behavior than the symmetrical single-photon case against the decoherence in a certain region.

DOI
10.1088/1612-202x/aa9aae

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I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantum teleportation) in certain parameter ranges spanned by the low transmissivities of the BSs and the small squeezing parameter of the input TMSVS.
We theoretically investigate the performance of multiphoton catalysis applied on the two-mode squeezed state by examining the entropy of entanglement, logarithmic negativity, Eistein-Podolsky-Rosen (EPR), and Hillery-Zubairy (HZ) correlations, and the fidelity of teleportation. It is found that the entanglement increases with the number of catalysis operations if the squeezing parameter is low initially. Our comparisons show that the HZ correlation presents a better performance than the EPR correlation for detecting the entanglement, and the improvement of HZ correlation definitely results in the improvement of entropy of entanglement rather than negativity; the region of enhanced EPR correlation is a subregion of all other entanglement properties. In addition, we consider the performances of the fidelity by comparing such operations applied before or after the amplitude damping channel. It is shown that the catalysis operation of m=n=1m=n=1m=n=1 before the channel presents the best performance in the initial-low squeezing regime. This may provide a useful insight for a long-distance quantum communication.
Abstract In this work, we propose a scheme for generating non-classical quantum catalyzed states, named Laguerre polynomial-weighted squeezed states, via inputting a single-mode squeezed vacuum state and an m -photon Fock state by quantum catalysis and two-mode squeezing. The non-classical properties of the generated catalyzed state are investigated using the degree of squeezing and Wigner function. It is found that these non-classical properties, including squeezing degree and the negativity of the Wigner function, can be improved and modulated by both squeezing parameters and the catalyzed photon number.
We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that the normalized factor is related to the two-variable Hermite polynomials. We then investigate the nonclassical properties in terms of Mandel's Q parameter, quadrature squeezing, second correlation, and the negativity of Wigner function (WF). It is shown that all these properties are related to the amplitude of coherent state, catalysis number and unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced as catalysis number and keeps a constant for single-photon catalysis. In addition, we examine the effect of decoherence by Wigner function, which show that the negative region, characteristic time of decoherence and structure of WF are affected by catalysis number and unbalanced BS. Our work provides a general analysis about how to prepare theoretically polynomials quantum states.