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Physical Review A

Distributing quantum states with finite lifetime

Stefano Maranò, Moe Z. Win

Published May 17, 2023• 10 citations
Publisher

Abstract

This paper considers a quantum node tasked with the teleportation of multiple information-carrying qubit (ICQ) streams, each to a different receiver, by means of entanglements, local operations, and classical communication. Our vision is that the node establishes entangled qubit pairs (EQPs) with the receivers before the arrival of ICQs, rather than waiting for their arrival. In this vein, the paper focuses on the class of protocols referred to as class $\mathcal{I}$ that instantaneously teleport arriving ICQs using preestablished EQPs, preventing arriving ICQs from decohering. The excess ratio ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ is introduced as a quantifier of the system resources per arriving ICQ, and ${\ensuremath{\varepsilon}}_{\mathrm{r}}=1$ is shown to be a critical threshold. With ${\ensuremath{\varepsilon}}_{\mathrm{r}}>1$: for arrival streams characterized by interarrivals stochastically larger than exponential random variables, any member of class $\mathcal{I}$ teleports all arriving ICQs after a finite transient. With ${\ensuremath{\varepsilon}}_{\mathrm{r}}<1$: for stationary ergodic arrival streams, there exists no protocol that teleports all arriving ICQs after a finite transient. This work thus establishes the ultimate limit for distributing quantum states with finite lifetime. Within class $\mathcal{I}$, a protocol referred to as fresh information delivery (FID) is introduced and its optimality is proven. The operational characteristic of FID is provided in terms of the tradeoff between the waiting time of the EQP before it is utilized for teleportation and the excess ratio. Numerical experiments, comparing the proposed FID protocol with alternatives, corroborate the theoretical results. The results in this paper can be used for designing quantum nodes, paving the way for the implementation of the future quantum internet.

DOI
10.1103/physreva.107.052413

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This paper considers a quantum node tasked with the teleportation of multiple information-carrying qubit (ICQ) streams, each to a different receiver, by means of entanglements, local operations, and classical communication. Our vision is that the node establishes entangled qubit pairs (EQPs) with the receivers before the arrival of ICQs, rather than waiting for their arrival. In this vein, the paper focuses on the class of protocols referred to as class I\mathcal{I}I that instantaneously teleport arriving ICQs using preestablished EQPs, preventing arriving ICQs from decohering. The excess ratio \ensuremathεr{\ensuremath{\varepsilon}}_{\mathrm{r}}\ensuremathεr​ is introduced as a quantifier of the system resources per arriving ICQ, and \ensuremathεr=1{\ensuremath{\varepsilon}}_{\mathrm{r}}=1\ensuremathεr​=1 is shown to be a critical threshold. With \ensuremathεr>1{\ensuremath{\varepsilon}}_{\mathrm{r}}>1\ensuremathεr​>1: for arrival streams characterized by interarrivals stochastically larger than exponential random variables, any member of class I\mathcal{I}I teleports all arriving ICQs after a finite transient. With \ensuremathεr<1{\ensuremath{\varepsilon}}_{\mathrm{r}}<1\ensuremathεr​<1: for stationary ergodic arrival streams, there exists no protocol that teleports all arriving ICQs after a finite transient. This work thus establishes the ultimate limit for distributing quantum states with finite lifetime. Within class I\mathcal{I}I, a protocol referred to as fresh information delivery (FID) is introduced and its optimality is proven. The operational characteristic of FID is provided in terms of the tradeoff between the waiting time of the EQP before it is utilized for teleportation and the excess ratio. Numerical experiments, comparing the proposed FID protocol with alternatives, corroborate the theoretical results. The results in this paper can be used for designing quantum nodes, paving the way for the implementation of the future quantum internet.
Transmitting unknown quantum states to distant locations is crucial for distributed quantum information protocols. The seminal quantum teleportation scheme achieves this feat while requiring prior maximal entanglement between the sender and receiver. In scenarios with noisy entangled states, optimal teleportation fidelity characterizes the efficacy of transmitting the state, demanding the proper selection of local operations at the sender's and receiver's ends. The complexity escalates further in long-range communication setups, prompting the consideration of a repeater-based approach, which incorporates arrays of nodes with multiple segments to facilitate the efficient transmission of quantum information. The fidelity of the communication line gets degraded even if a single segment is affected by noise. In such cases, the general wisdom employs the standard entanglement swapping protocol involving maximally entangled states across the noiseless segments and applying maximally entangled basis measurement at the corresponding nodes to achieve optimal fidelity. In this Letter, we propose a more efficient protocol for a certain class of noisy states, achieving the same fidelity as the standard protocol while consuming less amount of entanglement. Our approach ensures optimal teleportation fidelity even when the end-to-end state gets noisier, and thus promises efficient utility of quantum resources in repeater-based distributed quantum protocols.
Quantum information technology has the potential to revolutionize computing, communications, and security. To fully realize its potential, quantum processors with millions of qubits are needed, which is still far from being accomplished. Thus, it is important to establish quantum networks to enable distributed quantum computing to leverage existing and near-term quantum processors into more powerful resources. This paper introduces a protocol to distribute entanglements among quantum devices within classical-quantum networks with limited quantum links, enabling more efficient quantum teleportation in near-term hybrid networks. The proposed protocol uses entanglement swapping to distribute entanglements efficiently in a butterfly network, then classical network coding is applied to enable quantum teleportation while overcoming network bottlenecks and minimizing qubit requirements for individual nodes. Experimental results show that the proposed protocol requires quantum resources that scale linearly with network size, with individual nodes only requiring a fixed number of qubits. For small network sizes of up to three transceiver pairs, the proposed protocol outperforms the benchmark by using 17% fewer qubit resources, achieving 8.8% higher accuracy, and with a 35% faster simulation time. The percentage improvement increases significantly for large network sizes. We also propose a protocol for securing entanglement distribution against malicious entanglements using quantum state encoding through rotation. Our analysis shows that this method requires no communication overhead and reduces the chance of a malicious node retrieving a quantum state to 7.2%. The achieved results point toward a protocol that enables a highly scalable, efficient, and secure near-term quantum Internet.
Abstract In standard quantum teleportation, the receiver must wait for a classical message from the sender before subsequently processing the transmitted quantum information. However, in port-based teleportation (PBT), this local processing can begin before the classical message is received, thereby allowing for asynchronous quantum information processing. Motivated by resource-theoretic considerations and practical applications, we propose different communication models that progressively allow for more powerful decoding strategies while still permitting asynchronous distributed quantum computation, a salient feature of standard PBT. Specifically, we consider PBT protocols augmented by free classical processing and/or different forms of quantum pre-processing, and we investigate the maximum achievable teleportation fidelities under such operations. Our analysis focuses specifically on the PBT power of isotropic states, bipartite graph states, and symmetrized EPR states, and we compute tight bounds on the optimal teleportation fidelities for such states. We finally show that, among this hierarchy of communication models consistent with asynchronous quantum information processing, the strongest resource theory is equally as powerful as any one-way teleportation protocol for surpassing the classical teleportation threshold. Thus, a bipartite state can break the one-way classical teleportation threshold if and only if it can be done using the trivial decoding map of discarding subsystems.
Quantum information technology has the potential to revolutionize computing, communications, and security. To fully realize its potential, quantum processors with millions of qubits are needed, which are still far from being accomplished. Thus, it is important to establish quantum networks to enable distributed quantum computing to leverage existing and near-term quantum processors into more powerful resources. This paper proposes an efficient entanglement distribution protocol for classical-quantum networks with a limited number of quantum links, enabling quantum teleportation in near-term hybrid networks. The proposed protocol uses entanglement swapping and classical network coding to distribute entanglements efficiently while overcoming bottlenecks and minimizing qubit and link usage. Experimental results show that the proposed protocol requires quantum resources that scale linearly with network size, with individual nodes only requiring a fixed number of qubits. For small network sizes of up to three transceiver pairs, the proposed protocol outperforms the benchmark by using 17% fewer qubit resources, achieving 8.8% higher accuracy, and with a 35% faster simulation time. The percentage improvement increases significantly for large network sizes. We also propose a protocol for securing entanglement distribution against malicious entanglements using quantum state encoding through rotation. Our analysis shows that this method requires no communication overhead and reduces the chance of a malicious node retrieving the teleported state to 7.2%. The achieved results point toward a protocol that enables a highly scalable, efficient, and secure near-term quantum Internet.
This paper proposes a novel quantum networking protocol leveraging quantum teleportation for rapid quantum information transfer within a network. Traditional quantum network architectures suffer from limited transmission speeds due to the requirement of physically transporting qubits. This protocol overcomes this limitation by utilizing the quantum entanglement and Bell states to facilitate instantaneous information transfer, circumventing the need for direct qubit conveyance. The core of the protocol relies on establishing and maintaining entanglement between nodes, followed by a Bell state measurement and classical communication to reconstruct the quantum state at the destination. This design offers a significantly faster method for quantum information distribution compared to conventional approaches. The theoretical framework is presented with detailed mathematical formulations of the key steps, including the Bell state measurement, the process of quantum state transfer, and the necessary classical communication protocols. This work contributes to the advancement of quantum networking technology and provides a foundation for future high-speed quantum communication systems.
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.