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Physica Scripta

Beam splitter as controlled-Z gate for hybrid states

Mikhail S. Podoshvedov, Sergey A. Podoshvedov

Published May 12, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/add79a

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Laser Physics Letters•Aug 30, 2019•15 citations
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.
We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle the initial single-mode squeezed vacuum (SMSV) state with the photon state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity or reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. 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 the 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 that could increase the success probability of generating maximal hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
Abstract A protocol for quantum teleportation of an unknown single-rail qubit through the non-maximally entangled hybrid state is proposed. The hybrid quantum channel consists of continuous variable (CV) states of certain parity and photonic states and is characterized by two parameters: a squeezing parameter of single-mode squeezed vacuum state and the beam splitter (BS) parameter, on which the entangled state can be realized. The CV part of the hybrid state is in Alice’s location, while discrete variable half is controlled by Bob. A balanced BS is used to mix the CV part of the hybrid quantum state with an unknown optical single-rail qubit, followed by measurement of the number of photons in two measuring channels. Proper choice of the hybrid entangled state parameter values compensates for the initial amplitude distortion coefficient of the entangled state by the induced factor, so that Bob can obtain the initial qubit in the case of single photon measurement. With other measurement outcomes, Bob can obtain a qubit that has already undergone a unitary transformation, which he can use to teleport to other participants. We show that the proposed method is a generalization of quantum teleportation of single rail qubit via a nonlocal photon acting as a quantum channel.
Continuous variable (CV) entanglement refers to the type of entanglement of quantum wave-like systems that are described by continuous variables in an inherently infinite-dimensional space. It can become a crucial resource for quantum communication, sensing, and computation. We propose the mechanism of transfer of quantum entanglement (TQE) from a nonlocal photon to two initially separate single-mode squeezed vacuum (SMSV) states. The nonlocal photon is the only original quantum resource from which entanglement is transferred to CV states of a certain parity in a deterministic manner without them directly interacting with each other. Measurement-induced CV parity entanglement is tuned using initial squeezing and the beam splitter (BS) parameter, allowing us to estimate the probability of transfer of maximum entanglement at sufficiently high brightness to be 0.2344 for initial SMSV states. If, instead of the original SMSV states, we use those from which one photon is initially subtracted, then the heralded technique can turn the maximum entanglement probabilistic transfer protocol into a nearly deterministic one, the probability of which is >0.98. Such a perfect TQE from the nonlocal photon to a maximally parity-entangled CV state can be considered the most suitable for applications, since it preserves the trade-off between the probability of its implementation and brightness of the output non-Gaussian states.
We present a new method to entangle continuous variable (CV) states of certain parity and photonic states for the purpose of generating optical hybrid cluster (HC) states. To do it we introduce two families of the CV states of definite parity which stems from single mode squeezed vacuum (SMSV) state. Potential to apply the CV states of certain parity is high. We report on the generation of the even/odd Schrödinger cat state like (SCS-like) states whose fidelities with even/odd SCS of amplitude of [Formula: see text] are more of [Formula: see text], when 30,31 photons are detected in auxiliary mode of input SMSV state initially mixed with single photon. We show that the quantum efficiency of a photon number resolving (PNR) detector is crucial to maintaining the success rate of even/odd SCSs generator at an acceptable level. The scheme with delocalized photon implements deterministic imperfect entanglement operation between macro and micro states. We show that the beam splitter implements the two-qubits operation [Formula: see text] (CZ) for input CV states of definite parity and photonic states, provided that certain result is detected in measurement mode. An extension of the entangling operation for two entangled delocalized photons (TEDP) allows one to realize three-qubit HC state. Seven-qubit HC state is the result of conjunction of two three-qubit HC states through TEDP state.
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.