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Journal of Physics A Mathematical and Theoretical

Efficient quantum broadcast for an arbitrary number of receivers in noisy channels

Mohammad Bolokian, Ali A. Orouji, Monireh Houshmand

Published Aug 26, 2025• 1 citation
Publisher

Abstract

Abstract Quantum broadcast is a method for distributing known quantum information to multiple recipients at once. Although the no-cloning theorem prohibits copying unknown quantum states, it is still possible to transmit the same known state to different destinations. This research introduces two new approaches. The first approach allows a sender to broadcast a single qubit to n receivers using a specialized entangled state known as a 2 n -qubit cluster state. The paper illustrates this method with a detailed example for four receivers ( n = 4 ) and demonstrates its validity through implementation on the Qiskit platform. The second protocol, builds upon the first protocol and allows for broadcasting a particular class of n-qubit state to n receivers. The effects of different quantum noise types on the protocol are investigated, with the fidelity metric used to quantify the quality of broadcasted states over a noisy quantum channel. These new protocols offer more efficient ways to share quantum information, potentially paving the way for improved quantum communication networks and internet.

DOI
10.1088/1751-8121/adff41

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Abstract Quantum broadcast is a method for distributing known quantum information to multiple recipients at once. Although the no-cloning theorem prohibits copying unknown quantum states, it is still possible to transmit the same known state to different destinations. This research introduces two new approaches. The first approach allows a sender to broadcast a single qubit to n receivers using a specialized entangled state known as a 2 n -qubit cluster state. The paper illustrates this method with a detailed example for four receivers ( n = 4 ) and demonstrates its validity through implementation on the Qiskit platform. The second protocol, builds upon the first protocol and allows for broadcasting a particular class of n-qubit state to n receivers. The effects of different quantum noise types on the protocol are investigated, with the fidelity metric used to quantify the quality of broadcasted states over a noisy quantum channel. These new protocols offer more efficient ways to share quantum information, potentially paving the way for improved quantum communication networks and internet.
Due to the unavoidable interaction between the quantum channel and its ambient environment, it is difficult to generate and maintain the maximally entanglement. Thus, the research on multiparty information transmission via non-maximally entangled channels is of academic value and general application. Here, we utilize the non-maximally entangled channels to implement two multiparty remote state preparation schemes for transmitting different quantum information from one sender to two receivers synchronously. The first scheme is adopted to transmit two different four-qubit cluster-type entangled states to two receivers with a certain probability. In order to improve success probabilities of such multicast remote state preparation using non-maximally entangled channels, we put forward the second scheme, which deals with the situation that is a synchronous transfer of an arbitrary single-qubit state and an arbitrary two-qubit state from one sender to two receivers. In particular, its success probability can reach 100% in principle, and independent of the entanglement degree of the shared non-maximally entangled channel. Notably, in the second scheme, the auxiliary particle is not required.
Broadcast and multicast protocols are two branches of multi-party quantum communication. Implementing these protocols based on partial entanglement is of great practical importance since maximally entangled channels are not robust due to noise applied by the surrounding environment. Previous research has used global operators (i.e. operators which are applied on the qubits owned by different parties), which contradicts the concept of multi-party communication protocols. In this research, broadcast protocol and multicast protocol with two receivers are proposed using partially entangled channels. Then the protocols are extended to the case with an arbitrary number of receivers. In the proposed protocol, Alice shares a two-qubit maximally entangled state with each receiver, therefore the whole channel is a partially entangled state. Then, the proposed protocol is modified to be secure against eavesdroppers. Also, the effects of phase damping, bit flip, and phase damping noise on the broadcast protocol are examined and compared.
We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.
Abstract Quantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.
Quantum entanglement assisted with measurements provides various pathways to communicate information to parties within a network. In this work, we generalize a previous broadcasting protocol and present schemes to broadcast product and multipartite entangled quantum states, where in the latter case the sender can remotely add phase gates or abort distributing the states. We first focus on the broadcasting of product quantum states in a network, and generalize the basic protocol to include an arbitrary basis rotation and allow for multiple receivers and senders. We show how to add and delete senders from the network. The generalization also includes the case where a phase to be applied to the broadcast states is not known in advance but is provided to a sender encoded in another quantum state. Applications of broadcasting product states include authentication and three-state quantum cryptography. In the second part, we study the distribution of a single multiqubit state shared among several receivers entangled with multiqubit phase gates, which includes the graph states as an example. We show that by coordinating with the sender, the receivers can assist in performing remote, distributed measurement-based quantum computation with the Pauli-XXX basis measurement alone. As another application of this, we discuss the distribution of the multiqubit Greenberger-Horne-Zeilinger state.
The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, probabilistically sending an unknown qubit state to two receivers, sending different qubit states to two receivers, and sending qutrit states to two receivers. Finally, we discuss some applications of these protocols.