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arXiv:2209.02460 · Physica Scripta

Controlled quantum teleportation between discrete and continuous physical systems

Meryem El Kirdi, Abdallah Slaoui, Nada Ikken, Mohammed Daoud A, R. Ahl Laamara

Published Dec 19, 2022• 17 citations
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Abstract

Abstract Quantum teleportation of an unknown state basing on the interaction between discrete-valued states (DV) and continuous-valued states (CV) presented a particular challenge in quantum technologies. Here we consider the problem of controlled quantum teleportation of an amplitude-matched CV qubit, encoded by a coherent state of a varied phase as a superposition of the vacuum- and single-photon optical states among two distant partners Alice and Bob, with the consent of controller, Charlie. To achieve this task, we use an hybrid tripartite entangled state (interaction between the discrete and continuous variables states) as the quantum resource where the coherent part belongs to Alice, while the single-photon belongs to Bob and Charlie and the CV qubit is at the disposal of Alice. The discrete-continuous interaction is realized on highly transmissive beam-splitter. We have shown that the perfectly of teleportation fidelity depends on the phase difference between the phase of the state to teleport and the phase of the sender’s mode, we found that for a difference which approaches 0 or π , near perfect controlled quantum teleportation can be obtained in terms of the fidelity and independently of the amplitude α and the squeezing parameter ζ . Experimentally, this proposed scheme has been implemented using linear optical components such as beam splitter, phase shifters and photon counters.

DOI
10.1088/1402-4896/acacd2

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Abstract Quantum teleportation of an unknown state basing on the interaction between discrete-valued states (DV) and continuous-valued states (CV) presented a particular challenge in quantum technologies. Here we consider the problem of controlled quantum teleportation of an amplitude-matched CV qubit, encoded by a coherent state of a varied phase as a superposition of the vacuum- and single-photon optical states among two distant partners Alice and Bob, with the consent of controller, Charlie. To achieve this task, we use an hybrid tripartite entangled state (interaction between the discrete and continuous variables states) as the quantum resource where the coherent part belongs to Alice, while the single-photon belongs to Bob and Charlie and the CV qubit is at the disposal of Alice. The discrete-continuous interaction is realized on highly transmissive beam-splitter. We have shown that the perfectly of teleportation fidelity depends on the phase difference between the phase of the state to teleport and the phase of the sender’s mode, we found that for a difference which approaches 0 or π , near perfect controlled quantum teleportation can be obtained in terms of the fidelity and independently of the amplitude α and the squeezing parameter ζ . Experimentally, this proposed scheme has been implemented using linear optical components such as beam splitter, phase shifters and photon counters.
Quantum teleportation between polarized single-photon and phase-opposite coherent states is studied using a hybrid entangled resource and entangled coherent states. The polarized single-photon qubit represents a discrete-variable (DV) quantum system, whereas the phase-opposite coherent-state qubit constitutes a continuous-variable (CV) system. While teleportation from CV to DV can be achieved with near-unit success probability, the reverse process is usually limited to a maximum success probability of 1/21/21/2. We demonstrate that, by employing cross-Kerr nonlinearity together with passive linear optical components such as polarizing beam splitters, beam splitters, and phase shifters, almost perfect teleportation from DV to CV encodings can also be achieved.
We develop a quantum teleportation protocol of an unknown optical single rail qubit using a hybrid quantum channel composed of continuous variable (CV) states of certain parity. The quantum channel is characterized by two parameters: a squeezing parameter of single-mode squeezed vacuum (SMSV) state and the beam splitter (BS) parameter used to implement it. The CV part of the hybrid state belongs to Alice, while discrete variable (DV) half is controlled by Bob. The third parameter of the protocol is a parameter of the beam splitter, used to mix the CV components of the hybrid quantum state with unknown optical single-rail qubit. Even though the number of measurement results Alice sends may increase, Bob can obtain the original qubit half the time with an appropriate choice of parameter values. In almost half the remaining cases, Bob obtains the original qubit with distorted amplitudes, and both participants know the value of the distortion factors. This means that as the amount of classical information transmitted by Alice increases, they both gain greater access to partial information about the unitary transformations that the teleported qubits undergo, allowing Bob to continue using them or attempt to recover them to improve the protocol's efficiency. The proposed method is a generalization of quantum teleportation with a nonlocal photon used as a quantum channel and unknown single-rail optical qubit.
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.
The transfer of quantum information between physical systems of a different nature is a central matter in quantum technologies. Particularly challenging is the transfer between discrete and continuous degrees of freedom of various harmonic oscillator systems. Here we implement a protocol for teleporting a continuous-variable optical qubit, encoded by means of low-amplitude coherent states, onto a discrete-variable, single-rail qubit-a superposition of the vacuum and single-photon optical states-via a hybrid entangled resource. We test our protocol on a one-dimensional manifold of the input qubit space and demonstrate the mapping onto the equator of the teleported qubit's Bloch sphere with an average fidelity of 0.83±0.04. Our work opens up the way to the wide application of quantum information processing techniques where discrete- and continuous-variable encodings are combined within the same optical circuit.
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fidelity of the protocol. Final problem is reduced to finding a way to get rid of amplitude-distorting factor to restore the original qubit. Some strategies to increase the fidelity of the protocol are used. We show the teleportation can be implemented with arbitrary settings. Our approach is applicable to different basic number states of original unknown qubit. The scheme is realized by linear optics methods and requires an irreducible number of optical elements.
We propose and develop the theory of quantum teleportation of an unknown qubit based on the interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on the simultaneous displacement of the DV state on equal in absolute value, but opposite in sign displacement amplitudes by coherent components of the hybrid in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary modes. The relative phase of the displaced unknown qubit in the measurement number state basis can vary on opposite, depending on the parity of the basis states in the case of the negative amplitude of displacement that is akin to action of nonlinear effect on the teleported qubit. All measurement outcomes of the quantum teleportation are distinguishable, but the teleported state at Bob's disposal may acquire a predetermined amplitude-distorting factor. Two methods of getting rid of the factors are considered. The quantum teleportation is considered in various interpretations. A method for increasing the efficiency of quantum teleportation of an unknown qubit is proposed.