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arXiv:2504.00710 · IEEE Transactions on Information Theory

Entanglement Recycling in Two-Step Port-Based Teleportation

Piotr Kopszak, Dmitry Grinko, Adam Burchardt, Māris Ozols, Michał Studziński, Marek Mozrzymas

Published Jan 21, 2026• 0 citations
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Abstract

A protocol involving the repetitive (twofold, to be precise) application of PBT protocol to the same resource is studied. The quantities characterizing the resulting protocol, so-called \textit{two-step PBT}, namely \textit{enatnglement fidelity} and \textit{success probability} are provided for two scenarios, relying on application of pretty-good measurement, i.e. deterministic and probabilistic PBT with non-EPR resource. This results show that two-step PBT is an accurate protocol, provided the resource is sufficiently large. In particular, the deterministic two-step PBT obtains fidelity that is remarkably close to the optimal MPBT fidelity for teleportation of two quantum states. Additionally, the \textit{recycling fidelity}, i.e. the quantity characterizing the degradation of the resource state is calculated for repetitive application of probabilistic protocol, for both EPR and optimized resource, showing that entanglement recycling with two-step PBT is possible in the former case as well.

DOI
10.1109/tit.2026.3656762

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A protocol involving the repetitive (twofold, to be precise) application of PBT protocol to the same resource is studied. The quantities characterizing the resulting protocol, so-called \textit{two-step PBT}, namely \textit{enatnglement fidelity} and \textit{success probability} are provided for two scenarios, relying on application of pretty-good measurement, i.e. deterministic and probabilistic PBT with non-EPR resource. This results show that two-step PBT is an accurate protocol, provided the resource is sufficiently large. In particular, the deterministic two-step PBT obtains fidelity that is remarkably close to the optimal MPBT fidelity for teleportation of two quantum states. Additionally, the \textit{recycling fidelity}, i.e. the quantity characterizing the degradation of the resource state is calculated for repetitive application of probabilistic protocol, for both EPR and optimized resource, showing that entanglement recycling with two-step PBT is possible in the former case as well.
Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. In this protocol two spatially separated parties can teleport an unknown quantum state only by exploiting joint measurements on shared d−d-d−dimensional maximally entangled states (resource state) together with a state to be teleported and one way classical communication. In this paper we analyse degradation of the resource state after one round of PBT and implications for the recycling protocol for deterministic PBT introduced earlier. In the recycling protocol the main idea is to re-use the remaining resource state after one or many rounds of PBT for further processes of teleportation. It was stated by other authors that the recycling protocol is by arguing that the resource state does not degrade too much after each round of teleportation process. In particular, there is a claim that the fidelity between ideal resource state and its real version, each of them after one round of PBT, reaches asymptotically 1 when the number of shared entangled pairs tends to infinity. Here, considering original setup for the recycling protocol, we disprove these claims. We show the resource state is heavily distorted after even one round of PBT with fidelity not exceeding the value 1/d1/d1/d. This bound was obtained by referring only to Schwarz inequality and general properties of measurements exploited in the protocol. As additional results we present explicit formula for the mentioned fidelity involving group-theoretic parameters describing irreducible representations in the Schur-Weyl duality. For the first time, we also analyse the degradation of the resource state for the optimal PBT scheme and show its substantial distortion for all d≥2d\geq 2d≥2. (...)
Abstract Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. In this protocol two spatially separated parties can teleport an unknown quantum state only by exploiting joint measurements on number of shared d-dimensional maximally entangled states (resource state) together with a state to be teleported and one way classical communication. In this paper we analyse for the first time the recycling protocol for the deterministic PBT beyond the qubit case. In the recycling protocol the main idea is to re-use the remaining resource state after one or many rounds of PBT for further processes of teleportation. The key property is to learn how much the underlying resource state degrades after every round of the teleportation process. We measure this by evaluating quantum fidelity between respective resource states. To do so we first present analysis of the square-root measurements used by the sender in PBT by exploiting the symmetries of the system. In particular, we show how to effectively evaluate their square-roots and composition. These findings allow us to present the explicit formula for the recycling fidelity involving only group-theoretic parameters describing irreducible representations in the Schur–Weyl duality. For the first time, we also analyse the degradation of the resource state for the optimal PBT scheme and show its degradation for all d ⩾ 2. In the both versions, the qubit case is discussed separately resulting in compact expression for fidelity, depending only on the number of shared entangled pairs.
Abstract There are two types of port-based teleportation (PBT) protocols: deterministic—when the state always arrives to the receiver but is imperfectly transmitted and probabilistic—when the state reaches the receiver intact with high probability. We introduce the minimal set of requirements that define a feasible PBT protocol and construct a simple PBT protocol that satisfies these requirements: it teleports an unknown state of a qubit with success probability p succ = 1 − N + 2 2 N + 1 and fidelity 1 − O ( 1 N ) with the resource state consisting of N maximally entangled states. This protocol is not reducible from either the deterministic or probabilistic PBT protocol. We define the corresponding efficient superdense coding protocols which transmit more classical bits with fewer maximally entangled states. Furthermore, we introduce rigorous methods for comparing and converting between different PBT protocols.
Abstract Port-based teleportation (PBT) represents a variation of the standard quantum teleportation and is currently being employed and explored within the field of quantum information processing owing to its various applications. In this study, we focus on PBT protocol when the resource state is disrupted by local Pauli noises. Here, we fully characterise the channel of the noisy PBT protocol using Krauss representation. Especially, by exploiting the application of PBT for entanglement distribution necessary in realizing quantum networks, we investigate entanglement transmission through this protocol for each qubit considering noisy resource states, denoted as port-based entanglement teleportation (PBET). Finally, we derive upper and lower bounds for the teleported entanglement as a function of the initial entanglement and the noises. Our study demonstrates that quantum entanglement can be efficiently distributed by protocols utilizing large-sized resource states in the presence of noise and is expected to serve as a reliable guide for developing optimized PBET protocols. To obtain these results, we address that the order of entanglement of two qubit states is preserved through the local Pauli channel, and identify the boundaries of entanglement loss through this teleportation channel.
Port-based teleportation (PBT) is a form of quantum teleportation in which no corrective unitary is required on the part of the receiver. Two primary regimes exist—deterministic PBT in which teleportation is always successful, but is imperfect, and probabilistic PBT, in which teleportation succeeds with probability less than one, but teleportation is perfect upon a success. Two further regimes exist within each of these, in which the resource state used for the teleportation is fixed to a maximally entangled state or free to be optimized. Recent works have resolved the long-standing problem of efficiently implementing port-based teleportation, tackling the two deterministic cases for qudits. Here, we provide algorithms in all four regimes for qubits. Emphasis is placed on the practicality of these algorithms, where we give polynomial improvements in the known gate complexity for PBT, as well as an exponential improvement in the required number of ancillas (albeit in separate protocols). Our approach to the implementation of the square-root measurement in PBT can be directly generalized to other highly symmetric state ensembles. For certain families of states, such a framework yields efficient algorithms in the case in which the Petz-recovery algorithm for the square-root measurement runs in exponential time. Published by the American Physical Society 2024
In our work we propose a generalization of the port-based teleportation scheme, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob's side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where the resource state is maximally entangled. It turns out that the new scheme gives better performance than the optimal PBT protocol with the respective larger dimension of the port. We exploit the same number of maximally entangled states in the resource state as in the ordinary port-based teleportation with a number of measurements scaling polynomially in the number of shared maximally entangled states. To obtain our results, i.e. explicit expressions for the performance of the new scheme, we deliver novel mathematical tools concerning representation theory of the algebra of partially transposed permutation operators, where the transposition acts on more than one subsystem.