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arXiv:2606.03181

Generalised simultaneous transmission of arbitrary quantum states and classical information

Nicholas Zaunders, Timothy C. Ralph

quant-phSubmitted Jun 2, 2026• Announced Jun 3, 2026• 0 citations• Revised Jun 22, 2026 (v2)
v1 · Jun 2, 2026v2 · Jun 22, 2026v3 · Jun 23, 2026
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Abstract

We present a protocol which allows for arbitrary optical quantum states to simultaneously carry and transmit classical data, without sacrificing the integrity of either the quantum or classical information. Our scheme encodes classical information via displacements in the phase space prior to transmission and retrieves each classical symbol via a Gaussian continuous-variable teleportation. The original quantum state is then restored by guessing the the original displacement and performing the appropriate inverse operation. In the limit of sufficiently high classical signal and high squeezing, we show that our scheme is capable of perfectly reconstructing both the input classical signal and the input quantum state without loss of coherence. An example is given in terms of the transmission of a dual-rail Bell state.

Comments
4 pages, 2 figures. Submitted to PRL

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We present a protocol which allows for arbitrary optical quantum states to simultaneously carry and transmit classical data, without sacrificing the integrity of either the quantum or classical information. Our scheme encodes classical information via displacements in the phase space prior to transmission and retrieves each classical symbol via a Gaussian continuous-variable teleportation. The original quantum state is then restored by guessing the the original displacement and performing the appropriate inverse operation. In the limit of sufficiently high classical signal and high squeezing, we show that our scheme is capable of perfectly reconstructing both the input classical signal and the input quantum state without loss of coherence. An example is given in terms of the transmission of a dual-rail Bell state.
We propose a new quantum communication scheme using quantum coherent states. In our scheme, classical information and the secret key are transmitted simultaneously without any loss of secret key rate performance, while only the secret key is transmitted in the conventional protocol. In our protocol, classical information is first modulated by pulse amplitude modulation (PAM). The secret key is then mapped by random Gaussian modulation and is added to the PAM symbol. The receiver decodes the classical information, treating the Gaussian signal as additive noise. The classical symbol is discarded from the received state after successive decoding of the classical information, and the secret key is then distilled by conventional protocol. We demonstrate that after the classical symbol is discarded, the remaining system is identical to the conventional quantum key distribution system. Our proposed scheme provides the same secret key rate as that of the conventional quantum key distribution system and provides an additional data rate of classical information.
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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.
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