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Journal of the Optical Society of America B

Finite-dimensional quantum states generated by conditional measurements on beam splitters

Heng-Mei Li, Xue-xiang Xu, Hong-Yun Huang, Zhen Wang, Zhi-Long Wan, Hong‐Chun Yuan

Published Feb 7, 2020• 7 citations
Publisher

Abstract

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.

DOI
10.1364/josab.381747

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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 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.
A scheme is proposed to investigate the non-classical states generated by a quantum scissors device (QSD) operating on the the cavity mode of an optomechanical system. When the catalytic QSD acts on the cavity mode of the optomechanical system, the resulting state contains only the vacuum, single-photon and two-photon states depending upon the coupling parameter of the optomechanical system as well as the transmission coefficients of beam splitters (BSs). Especially, the output state is just a class of multicomponent cat state truncations at time t = 2π by choosing the appropriate value of coupling parameter. We discuss the success probability of such a state and the fidelity between the output state and input state via QSD. Then the linear entropy is used to investigate the entanglement between the two subsystems, finding that QSD operation can enhance their entanglement degree. Furthermore, we also derive the analytical expression of the Wigner function (WF) for the cavity mode via QSD and numerically analyze the WF distribution in phase space at time t = 2π. These results show that the high non-classicality of output state can always be achieved by modulating the coupling parameter of the optomechanical system as well as the transmittance of BSs.
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.
The entanglement improvement is theoretically investigated when applying a single-side quantum scissors (SSQS) with a local squeezing operation and two-asymmetrical beam splitters (BSs) to one mode of an input two-mode squeezed vacuum state (TMSV). It is found that the gain factor can be significantly enhanced with the increasing of local squeezing parameter at the expense of the success probability. The entanglement can also be further improved adjusting the local-squeezing or the transmissivity of BSs in a small initial squeezing region. In addition, our scheme is robust against the photon loss in TMSV. The improved effect becomes more obvious due to the presence of local squeezing. However, the case is not true for a more realistic SSQS. In both cases, the asymmetric BSs play a positive role for the entanglement improvement. These results suggest that the squeezing-based SSQS at single-photon level is beneficial to effectively improve the entanglement, which may have potential applications in quantum communication.
We present a scheme of quantum state truncation in the Fock basis (quantum scissors), based on the combined action of a nondegenerate optical parametric amplifier and a beam splitter. Differently from previously proposed linear-optics-based quantum scissors devices, which depend on reliable Fock state sources, our scheme requires only readily available Gaussian states, such as coherent state inputs (vacuum state included). A truncated state is generated after performing photodetections in the global state. We find that, depending on which output ports each of the two photodetectors is positioned, different types of truncated states may be produced: (i) states having a maximum Fock number of NNN, or (ii) states having a minimum Fock number NNN. In order to illustrate our method, we discuss an example having as input states a coherent state in the beam splitter and vacuum states in the amplifier, and show that the resulting truncated states display nonclassical properties, such as sub-Poissonian statistics and squeezing. We quantify the nonclassicality degree of the generated states using the Wigner-Yanase skew information measure. For complementarity, we discuss the efficiency of the protocol, e.g., generation probability as well as the effects of imperfections such as the detector's quantum efficiency and dark counts rate.
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.