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arXiv:2412.15011 · Quantum Science and Technology

Quantum teleportation of cat states with binary-outcome measurements

Jingyan Feng, Mohan Zhang, Matteo Fadel, Tim Byrnes

Published Jul 29, 2025• 0 citations
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Abstract

Abstract We propose a teleportation protocol involving beam splitting operations and binary-outcome measurements, such as parity measurements. These operations have a straightforward implementation using the dispersive regime of the Jaynes–Cummings Hamiltonian, making our protocol suitable for a broad class of platforms, including trapped ions, circuit quantum electrodynamics and acoustodynamics systems. In these platforms homodyne measurements of the bosonic modes are less natural than dispersive measurements, making standard continuous variable teleportation unsuitable. In our protocol, Alice is in possession of two bosonic modes and Bob a single mode. An entangled mode pair between Alice and Bob is created by performing a beam splitter operation on a cat state. An unknown qubit state encoded by cat states is then teleported from Alice to Bob after a beamsplitting operation, measurement sequence, and a conditional correction. In the case of multiple measurements, near-perfect fidelity can be obtained. We discuss the optimal parameters in order to maximize the fidelity under a variety of scenarios.

DOI
10.1088/2058-9565/adf572

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Abstract We theoretically implement the protocol of continuous variable quantum teleportation wherein Alice and Bob share a state built by a linear beam splitter as general two-mode Gaussian entangled state. Using the non-classicality and purity of the two single-mode Gaussian states employed initially at the input of the beam splitter, the unknown state teleportation protocol is explicitly implemented in terms of squeezing and phase space quadratures. We show that fidelity of the teleported state is maximal when the gain factor g is equal to 1 and gradually decreases when g deviates from 1 on either side. We further find that teleportation fidelity decreases when one of the input states of the beam splitter is replaced by the state of thermal photons.
We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.
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We investigate theoretically quantum teleportation by means of the number-sum and phase-difference variables. We show that a unitary beam-splitter transformation turns two-mode Fock-states into close-to-maximally entangled states, in this case close approximations of the relative-phase eigenstates. These states could be created experimentally using on-demand single-photon sources, but also with any second-quantized bosonic system (e.g., trapped ions, Bose-Einstein condensates). We show that such ``quasi-EPR'' states can yield near-unity fidelity for the teleportation of coherent states and of ``Schr\"odinger cat'' states.
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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.