Multiport based teleportation – transmission of a large amount of quantum information

Kopszak, Piotr; Mozrzymas, Marek; Studziński, Michał; Horodecki, Michał

doi:10.22331/q-2021-11-11-576

“…We start our discussion by showing that any teleportation protocol is equivalent to a quantum state discrimination problem: the fidelity in the former is proportional to the success probability in the latter. This result generalizes the known relationship between fidelity and a state discrimination success probability for port-based teleportation, which was proved in [21,22,3], and applied to generalized port-based teleportation protocols in [23,28].…”

Section: Teleportation and State Discriminationsupporting

confidence: 75%

On the Duality of Teleportation and Dense Coding

Chitambar,

Leditzky

2024

IEEE Trans. Inform. Theory

1

0

View full text Add to dashboard Cite

Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially depends on the quality of the pre-shared entanglement. In this work, we revisit the problem of using noisy entanglement for the task of teleportation. We first show how this problem can be rephrased as a state discrimination problem. In this picture, a quantitative duality between teleportation and dense coding emerges in which every Alice-to-Bob teleportation protocol can be repurposed as a Bob-to-Alice dense coding protocol, and the quality of each protocol can be measured by the success probability in the same state discrimination problem. One of our main results provides a complete characterization of the states that offer no advantage in one-way teleportation protocols over classical states, thereby offering a new and intriguing perspective on the long-standing open problem of identifying such states. This also yields a new proof of the known fact that bound entangled states cannot exceed the classical teleportation threshold. Moreover, our established duality between teleportation and dense coding can be used to show that the exact same states are unable to provide a non-classical advantage for dense coding as well. We also discuss the duality from a communication capacity point of view, deriving upper and lower bounds on the accessible information of a dense coding protocol in terms of the fidelity of its associated teleportation protocol. A corollary of this discussion is a simple proof of the previously established fact that bound entangled states do not provide any advantage in dense coding. I. INTRODUCTIONQuantum teleportation [4] is one of the most important protocols in quantum information theory. It provides the backbone for a number of applications such as quantum communication [5], long-distance entanglement distribution via repeaters [7], and quantum computation [12]. From a fundamental perspective, teleportation beautifully demonstrates the interplay between different quantum resources: one communication primitive, a qubit channel, can be simulated using two other communication primitives, pre-shared entanglement and a two-bit classical channel. Consequently, universal distributed quantum computation can be achieved using preshared entanglement along with local operations and classical communication (LOCC). The rich study of entanglement and LOCC within quantum information science was largely due to this realization [19].

show abstract

“…We start our discussion by showing that any teleportation protocol is equivalent to a quantum state discrimination prob-lem: the fidelity in the former is proportional to the success probability in the latter. This result generalizes the known relationship between fidelity and a state discrimination success probability for port-based teleportation, which was proved in [19,20,2], and applied to generalized port-based teleportation protocols in [21,26].…”

Section: Teleportation and State Discriminationsupporting

confidence: 75%

On the Duality of Teleportation and Dense Coding

Chitambar¹,

Leditzky²

2023

Preprint

View full text Add to dashboard Cite

Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially depends on the quality of the pre-shared entanglement. In this work, we revisit the problem of using noisy entanglement for the task of teleportation. We first show how this problem can be rephrased as a state discrimination problem. In this picture, a quantitative duality between teleportation and dense coding emerges in which every Alice-to-Bob teleportation protocol can be repurposed as a Bob-to-Alice dense coding protocol, and the quality of each protocol can be measured by the success probability in the same state discrimination problem. One of our main results provides a complete characterization of the states that offer no advantage in one-way teleportation protocols over classical states, thereby offering a new and intriguing perspective on the long-standing open problem of identifying such states. This also yields a new proof of the known fact that bound entangled states cannot exceed the classical teleportation threshold. Moreover, our established duality between teleportation and dense coding can be used to show that the exact same states are unable to provide a non-classical advantage for dense coding as well. We also discuss the duality from a communication capacity point of view, deriving upper and lower bounds on the accessible information of a dense coding protocol in terms of the fidelity of its associated teleportation protocol. A corollary of this discussion is a simple proof of the previously established fact that bound entangled states do not provide any advantage in dense coding.

show abstract

“…Having explicit values of fidelity for teleported state after every round of the recycling protocol would allow for direct comparison with other existing protocols for teleporting a number of states. One of such possibility is for example nonand optimal version of multi-PBT schemes introduced and investigated in a series of papers [17,23,33,35]. This however, requires proving and computing new properties of the recycling scheme which are out of scope of this manuscript.…”

Section: Discussion and Further Researchmentioning

confidence: 99%

Square-root measurements and degradation of the resource state in port-based teleportation scheme

Studziński

¹

,

Mozrzymas²,

Kopszak³

2022

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

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 $d\geq 2$. 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.

show abstract

Multiport based teleportation – transmission of a large amount of quantum information

Cited by 13 publications

References 25 publications

On the Duality of Teleportation and Dense Coding

On the Duality of Teleportation and Dense Coding

On the Duality of Teleportation and Dense Coding

Square-root measurements and degradation of the resource state in port-based teleportation scheme

Contact Info

Product

Resources

About