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arXiv:2610.16198

Time-Frequency Continuous-Variable Quantum Teleportation with Single Photons

Mohamed Meguebel, Nadia Belabas, Nicolas Fabre

quant-phSubmitted Oct 12, 2026• Announced Oct 13, 2026• 0 citations
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Abstract

Quantum teleportation, a key building block for quantum technologies, enables distant parties, Alice and Bob, to transfer an unknown quantum state using entanglement, local operations, and classical communication. In this work, we propose a quantum teleportation protocol for single-photon time-frequency continuous variables, where time is the time of arrival at a detector. We detail the operational requirements of the protocol, notably the nonlinear interactions needed for the photon-photon time-frequency entangling gate. By explicitly treating the detector position as the reference frame for time of arrival, we show that, even with ideal classical and quantum channels, the input-output fidelity is not unity unless the receiving party can correct the detector-position mismatch. This results in a trade-off between teleportation fidelity and the temporal bandwidth of the input photon wavepacket. The protocol itself can be used for remote detector synchronization. In particular, we show that time-frequency cat and Gottesman-Kitaev-Preskill states provide an internal temporal ruler through fidelity revivals. We further derive the classical and best-copy fidelity thresholds for single-photon Gaussian wavepackets, finding that the relevant vacuum-equivalent shot noise is input-dependent, in contrast with quadrature-based continuous-variable quantum teleportation. Our proposal derives from a quantum theory of space-time events, whereafter we establish space as a reference for the time degree of freedom, thereby grounding our work in ongoing research on reference frames and superselection rules in quantum optics and quantum information. Beyond protocols harnessing time-frequency continuous variables of single photons, this work points toward remote synchronization in quantum communication architectures.

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Quantum teleportation, a key building block for quantum technologies, enables distant parties, Alice and Bob, to transfer an unknown quantum state using entanglement, local operations, and classical communication. In this work, we propose a quantum teleportation protocol for single-photon time-frequency continuous variables, where time is the time of arrival at a detector. We detail the operational requirements of the protocol, notably the nonlinear interactions needed for the photon-photon time-frequency entangling gate. By explicitly treating the detector position as the reference frame for time of arrival, we show that, even with ideal classical and quantum channels, the input-output fidelity is not unity unless the receiving party can correct the detector-position mismatch. This results in a trade-off between teleportation fidelity and the temporal bandwidth of the input photon wavepacket. The protocol itself can be used for remote detector synchronization. In particular, we show that time-frequency cat and Gottesman-Kitaev-Preskill states provide an internal temporal ruler through fidelity revivals. We further derive the classical and best-copy fidelity thresholds for single-photon Gaussian wavepackets, finding that the relevant vacuum-equivalent shot noise is input-dependent, in contrast with quadrature-based continuous-variable quantum teleportation. Our proposal derives from a quantum theory of space-time events, whereafter we establish space as a reference for the time degree of freedom, thereby grounding our work in ongoing research on reference frames and superselection rules in quantum optics and quantum information. Beyond protocols harnessing time-frequency continuous variables of single photons, this work points toward remote synchronization in quantum communication architectures.
We present a linear optical protocol for teleporting and correcting both temporal and frequency errors in two time–frequency qubit states. The first state is the frequency (or time-of-arrival) cat qubit, which is a single photon in a superposition of two frequencies (or time-of-arrival), while the second is the time–frequency Gottesman–Kitaev–Preskill (GKP) state, which is a single photon with a frequency comb structure. The proposed optical scheme could be valuable for reducing the error rate in quantum communication protocols involving one of these qubits.
We present a linear optical protocol for teleporting and correcting both temporal and frequency errors in two time-frequency qubit states. The first state is the frequency (or time-of-arrival) cat qubit, which is a single photon in a superposition of two frequencies (or time-of-arrival), while the second is the time-frequency Gottesman-Kitaev-Preskill (GKP) state, which is a single photon with a frequency comb structure. The proposed optical scheme could be valuable for reducing error rate in quantum communication protocols involving one of these qubits.
ABSTRACT We propose a setup for teleportation of continuous quantum variables which is optimized for teleportation ofsqueezed coherent states. Our scheme is a modified version of the original setup proposed by Braunstein andKimble [Phys. Rev. Lett. 80, 869, 1998] and it involves an unbalanced beam splitter on the sender's side and asingle mode squeezer on receiver's side. We show that the quality of the teleportation can be evaluated by meansof a fidelity of entanglement swapping and we prove that our modified setup and the original Braunstein-Kimblesetup are equivalent with respect to this fidelity measure.Keywords: Quantum teleportation, squeezed states, completely positive maps, fidelity 1. INTRODUCTION Quantum teleportation, a disembodied transfer of a quantum state between two distant parties, is perhaps themost remarkable and exciting development in the rapidly growing field of quantum information processing. Intheir seminal paper, Bennett et al.1 proposed a protocol for teleportation of a single qubit from the sender Aliceto the receiver Bob. The information about the teleported state is sent to Bob via dual classical and quantumEPR channels. The latter is established by a maximally entangled state shared by Alice and Bob.Recently, there has been much interest in quantum information processing with continuous quantum van-ables. Here, the focus is on systems with infinite dimensional Hubert spaces such as quantized electromagneticfield. Teleportation of continuous quantum variables was first considered by Vaidman,2 and an experimentallyfeasible setup was suggested by Braunstein and Kimble.3 Subsequent experiment4 demonstrated that theteleportation of a single mode of optical field is fully within the reach of current technology. Since then, manyauthors discussed various aspects of the teleportation,5'° including fidelity of teleportation of various quantumstates and influence of losses on the degradation of the quantum channel.Besides teleportation, many other protocols developed originally in the framework of discrete quantum van-ables, have been successfully formulated also for continuous variables. These include quantum cloning,11'3quantum
Quantum teleportation allows for the transfer of arbitrary, in principle, unknown quantum states from a sender to a spatially distant receiver, who share an entangled state and can communicate classically. It is the essence of many sophisticated protocols for quantum communication and computation. In order to realize flying qubits in these schemes, photons are an optimal choice. However, teleporting a photonic qubit has been limited due to experimental inefficiencies and restrictions. Major disadvantages have been the probabilistic nature of both entangled resource states and linear-optics Bell-state measurements (BSM), as well as the need for post-selecting the successful events by destroying the teleported qubit. Here, all the above limitations are overcome through a totally distinct, “hybrid” approach: continuous-variable (CV) quantum teleportation of a discrete-variable, photonic qubit. The strength of CV teleportation lies in the on-demand availability of the quadrature-entangled states and the completeness of a BSM in the quadrature bases using linear optics and homodyne detections; this enables fully deterministic, unconditional teleportation of photonic qubits. We implement this kind of “hybrid” teleportation by utilizing a very recent, advanced technology: a broadband CV teleporter and a narrow-band qubit compatible with the teleporter.
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.
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.