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Laser Physics Letters

Measurement-induced nonclassical state from two-mode squeezed vacuum states via beam splitter and its entanglement properties

Heng-Mei Li, Xue-xiang Xu, Hong‐Chun Yuan, Xiang‐Guo Meng

Published Aug 30, 2019• 15 citations
Publisher

Abstract

Abstract A theoretical scheme of generating a new kind of two-mode non-Gaussian entangled state is presented by means of beam splitters (BSs) and conditional measurement. Here, after detecting photon numbers at the output port of each BS with two kinds of two-mode squeezed vacuum-state inputs, the output state is proved to be two-variable Hermite polynomial excited squeezed vacuum states. Its success probability of detection, namely, normalization factor, is derived in compact expression related to the Jacobi polynomials. Based on the general expression of expectation value, the statistical properties are discussed by exploring the cross-correlation function and anti-bunching effect. The entanglement properties are also investigated by using the Shchukin–Vogel criteria and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the output state can be enhanced with the increasing photon detection number under the condition of simultaneously detecting the same photon number at the two output ports, which may have good potential for applications in the field of quantum information processing.

DOI
10.1088/1612-202x/ab3c5a

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Abstract A theoretical scheme of generating a new kind of two-mode non-Gaussian entangled state is presented by means of beam splitters (BSs) and conditional measurement. Here, after detecting photon numbers at the output port of each BS with two kinds of two-mode squeezed vacuum-state inputs, the output state is proved to be two-variable Hermite polynomial excited squeezed vacuum states. Its success probability of detection, namely, normalization factor, is derived in compact expression related to the Jacobi polynomials. Based on the general expression of expectation value, the statistical properties are discussed by exploring the cross-correlation function and anti-bunching effect. The entanglement properties are also investigated by using the Shchukin–Vogel criteria and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the output state can be enhanced with the increasing photon detection number under the condition of simultaneously detecting the same photon number at the two output ports, which may have good potential for applications in the field of quantum information processing.
Abstract In this work, we present a theoretical scheme for generating a new kind of tunable non-Gaussian entangled state, by means of beam splitters and multi-photon conditional measurement with two-mode squeezed vacuum state (TMSVS) inputs. The output state is proven to be two-variable Hermite polynomial excited squeezed vacuum states, whose success probability of detection relates to the Jacobi polynomials. We then mainly study the entanglement properties of the output state for the symmetric case quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. It is shown that the entropy of entanglement is valid for verifying the improvement of entanglement within a certain range of squeezing parameter and transmissivity, and the resulting state case may possess a stronger correlation than the initial TMSVS by increasing the transmissivity or photon number of detection. In addition, the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality for the output state is also evaluated in terms of Wigner representation in phase space. It is found that the negative region of Wigner function distribution becomes more visible with the increase of the photon number of detection, and the degree of the violation of the CHSH inequality significantly increases as the photon number of detection for the symmetrical case increases. The resulting state with highly nonclassical characteristics will provide a useful application in the fields of quantum information processing.
A scheme for conditional generating Hermite polynomial excited squeezed vacuum states (HPESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output channels, the conditional state in the other output channel is just a HPESVS. To exhibit a number of nonclassical effects and non-Gaussianity, we mainly investigate the photon number distribution, sub-Poissonian distribution, quadrature component distribution, and Wigner function of the conditional HPESVS. We find that its nonclassicality closely relates to the control parameter of the BS, the squeezed parameter of TMSVS, and the photon number of conditional measurement. These further demonstrate that performing the conditional measurement on a BS is an effective approach to generate non-Gaussian state.
In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.
Abstract We theoretically put forward a scheme to generate a new kind of the non-Gaussian state—two-mode squeezed Laguerre-polynomial-excited vacuum state (TMS-LPEVs) by using two beam splitters and conditional measurements with two kinds of TMS states inputs. It is interesting that the squeezed Bell state can be considered as a special case of TMS-LPEVs. Then we further examine its properties according to the entanglement entropy, the Einstein–Podolsky–Rosen correlation and the squeezing degree. It is found that for small auxiliary squeezing parameter r and high transmissivity, the entanglement entropy can be enhanced by single-photon measurement. When optimized over transmissivity, multiphoton measurements are beneficial to the improvement of the squeezing property and the teleportation fidelity in the region of larger λ accompanied by small auxiliary squeezing. More significantly, one can use a smaller squeezing parameter r to realize the improvements of the entanglement and the teleportation fidelity. These results may provide guidance for the implementation of experiments in quantum information and quantum computation.
Abstract We use the quadrature measurement to generate the novel nonclassical states via the beam splitter with two input states, i.e., a Fock state and a vacuum state. It is interesting to find that the desired target states are the Hermite polynomial excited vacuum states. Our results have shown that the zero-position detection for the position detector, the little photon number in the input state, and the high transmittance of the beam splitter (BS) are beneficial to improve the detection efficiency of finding the output states. The proposed states quantum statistical properties and squeezing effects are also studied in detail via different criteria. Our numerical analysis demonstrates that the output quantum states are new nonclassical states. Compared with the method of photon catalysis, position detection is easier to realize in experiments. Therefore, the results in this paper shall provide theoretical support for the experimental generation of several new nonclassical states.
Abstract We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle an initial single-mode squeezed vacuum (SMSV) state with a photonic state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity and reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. The maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled − Z CZ − operation using the BS with appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3 . We also propose to use new continuous variable (CV) states of definite parity, which could increase the success probability of generating the maximum hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.