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Laser Physics Letters

Entanglement improvement of entangled coherent state via multiphoton catalysis

Weidong Zhou, Wei Ye, Cunjin Liu, Liyun Hu, Sanqiu Liu

Published May 4, 2018• 25 citations
Publisher

Abstract

Abstract Based on the conditional measurement and beam splitters, multi-photon catalysis is introduced to each mode of even entangled coherent states (EECSs). The resulted states belong to a kind of Laguerre polynomials excited EECSs. Then the entanglement properties of resulted state are examined according to EPR correlation, concurrence and the teleportation fidelity. For the symmetrical beam splitters, these three quantities can be improved by multi-photon catalysis (⩾3) and only EPR correlation can be enhanced by zero-photon catalysis. Our optimal results over transmissivities of beam splitters show that the unit concurrence can be achieved for all non-zero photon catalysis which indicates that the optimized output approaches Bell-type state. In addition, two single-photon catalysis and zero-photon catalysis present better performance for the improvement of both the EPR correlation and the teleportation fidelity in small and large amplitude regions, respectively. Particularly, it is interesting to notice that both of them can be optimized to be constant for zero-photon catalysis when the amplitude exceeds a certain threshold.

DOI
10.1088/1612-202x/aaba4f

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Abstract Based on the conditional measurement and beam splitters, multi-photon catalysis is introduced to each mode of even entangled coherent states (EECSs). The resulted states belong to a kind of Laguerre polynomials excited EECSs. Then the entanglement properties of resulted state are examined according to EPR correlation, concurrence and the teleportation fidelity. For the symmetrical beam splitters, these three quantities can be improved by multi-photon catalysis (⩾3) and only EPR correlation can be enhanced by zero-photon catalysis. Our optimal results over transmissivities of beam splitters show that the unit concurrence can be achieved for all non-zero photon catalysis which indicates that the optimized output approaches Bell-type state. In addition, two single-photon catalysis and zero-photon catalysis present better performance for the improvement of both the EPR correlation and the teleportation fidelity in small and large amplitude regions, respectively. Particularly, it is interesting to notice that both of them can be optimized to be constant for zero-photon catalysis when the amplitude exceeds a certain threshold.
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.
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.
Abstract Multiphoton catalysis is a non-Gaussian operation which has aroused interest recently in quantum information processing. There are two schemes of multiphoton catalysis in the current literature: one uses a beam splitter, while the other uses an optical parametric amplifier. We derive the catalysis operator in the Fock basis for each scheme and find a close relationship between them. We propose to enhance quantum entanglement of the two-mode squeezed vacuum state by performing two-mode multiphoton catalysis independently using two beam splitters. We calculate the optimal entanglement, which is maximized over two independent transmissivities, for the catalyzed states with various pairs of catalysis photon numbers, and find that in each case entanglement is enhanced only when the squeezing parameter is below a certain threshold. We also find that the optimal entanglement is nonzero in the limit of low squeezing, and deduce the analytical forms of the limiting catalyzed state and its entanglement in each case from numerical coefficients.
Abstract We propose a scheme to generate a new kind of non-Gaussian state—the Laguerre polynomial excited coherent state (LPECS)—by using multiphoton catalysis with coherent state input. The nonclassical properties of the LPECS are studied in terms of nonclassical depth, Mandel’s parameter, second-order correlation, quadrature squeezing, and the negativity of the Wigner function (WF). It is found that the LPECS is highly nonclassical and its nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and the parameters of the unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced by increasing the catalysis photon number. In addition, we examine the effect of decoherence using the WF, which shows that the negative region, the characteristic time of decoherence, and the structure of the WF are affected by catalysis photon number and the parameters of the unbalanced BS. Our work provides general analysis on how to prepare polynomial quantum states, which may be useful in the fields of quantum information and quantum computation.
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.
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.