Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0107132 · Physical Review Letters

Teleportation as a Depolarizing Quantum Channel, Relative Entropy, and Classical Capacity

Garry Bowen, Sougato Bose

Published Dec 4, 2001• 264 citations
arXivHTMLPDF

Abstract

We show that standard teleportation with an arbitrary mixed state resource is equivalent to a generalized depolarizing channel with probabilities given by the maximally entangled components of the resource. This enables the usage of any quantum channel as a generalized depolarizing channel without additional twirling operations. It also provides a nontrivial upper bound on the entanglement of a class of mixed states. Our result allows a consistent and statistically motivated quantification of teleportation success in terms of the relative entropy and this quantification can be related to a classical capacity.

DOI
10.1103/physrevlett.87.267901

Related papers

Teleportation with a mixed state of four qubits and the generalized singlet fraction

Ye Yeo

Recently, an explicit protocol ${\mathcal{E}}_{0}$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. 96, 060502 (2006)]. Here, we show that ${\mathcal{E}}_{0}$ with an arbitrary four-qubit mixed-state resource $\ensuremath{\Xi}$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction $\mathcal{G}[\ensuremath{\Xi}]$ and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that $\mathcal{G}[\ensuremath{\Xi}]>1∕2$. In addition, we conjecture that when $\mathcal{G}[\ensuremath{\Xi}]<1∕4$, then no entanglement could be teleported. It is shown that to determine the usefulness of $\ensuremath{\Xi}$ for ${\mathcal{E}}_{0}$, it is necessary to analyze $\mathcal{G}[\ensuremath{\Xi}]$.

arXiv:quant-ph/0607108•Physical Review A•Nov 6, 2006•36 citations

Quantum Teleportation: from Pure to Mixed States and Standard to Optimal

Sergio A Albeverio, S.M. Fei, Wen‐Li Yang

Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.

arXiv:quant-ph/0308009•Aug 1, 2003•0 citations

Relevance of rank for a mixed state quantum teleportation resource

K. G. Paulson, S. V. M. Satyanarayana

Mixed entangled states are generic resource for quantum teleportation. Optimal teleportation fidelity measures the success of quantum teleportation. The relevance of rank in the teleportation process is investigated by constructing three new maximally entangled mixed states (MEMS) of different ranks. Linear entropy, concurrence, optimal teleportation fidelity and Bell function are obtained for each of these states analytically. It is found that mixed states with higher rank are better resource for teleportation. In order to achieve a fixed value of optimal teleportation fidelity, we find that low rank states must have high concurrence. Further, for each of ranks 2, 3 and 4, we numerically generate 30000 maximally entangled mixed states. The analysis of these states reveals the existence of a rank dependent upper bound on optimal teleportation fidelity for a fixed purity. In order to achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a rank dependent lower bound on concurrence. MEMS are classified in terms of their degree of nonlocality. The results are found to be same with logarithmic negativity used as a measure of entanglement.

arXiv:1308.2815•Quantum Information and Computation•Oct 1, 2014•3 citations

Quantum channels with correlated noise and entanglement teleportation

Ye Yeo

Motivated by the results of Macchiavello and Palma on entanglement-enhanced information transmission over a quantum channel with correlated noise, we demonstrate how the entanglement teleportation scheme of Lee and Kim gives rise to two uncorrelated generalized depolarizing channels. In an attempt to find a teleportation scheme that yields two correlated generalized depolarizing channels, we discover a teleportation scheme that allows one to learn about the entanglement in an entangled pure input state, without decreasing the amount of entanglement associated with it.

arXiv:quant-ph/0211084•Physical Review A•May 28, 2003•10 citations

Uncertainties of the standard quantum teleportation channel

Zhihua 志华 Zhang 章, Zehao Guo, Zhipeng 志鹏 Qiu 邱

Abstract From the perspective of state-channel interaction, standard quantum teleportation can be viewed as a communication process characterized by both input and output, functioning as a quantum depolarizing channel. To achieve a precise quantification of the quantumness introduced by this channel, we examine its uncertainties, which encompass both state-dependent and state-independent uncertainties. Specifically, for qudit systems, we provide general formulas for these uncertainties. We analyze the uncertainties associated with standard quantum teleportation when induced by isotropic states, Werner states, and X-states, and we elucidate the correlation between these uncertainties and the parameters of the specific mixed states. Our findings demonstrate the validity of quantifying these uncertainties.

Chinese Physics B•Feb 5, 2025•1 citation

Teleportations of Mixed States and Multipartite Quantum States

Chang‐shui Yu, Yahong Wang, He‐Shan Song

In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. If a non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1−(1− C 2 ) 1/2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation, Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.

Communications in Theoretical Physics•Jun 1, 2007•4 citations
We show that standard teleportation with an arbitrary mixed state resource is equivalent to a generalized depolarizing channel with probabilities given by the maximally entangled components of the resource. This enables the usage of any quantum channel as a generalized depolarizing channel without additional twirling operations. It also provides a nontrivial upper bound on the entanglement of a class of mixed states. Our result allows a consistent and statistically motivated quantification of teleportation success in terms of the relative entropy and this quantification can be related to a classical capacity.
Recently, an explicit protocol E0{\mathcal{E}}_{0}E0​ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. 96, 060502 (2006)]. Here, we show that E0{\mathcal{E}}_{0}E0​ with an arbitrary four-qubit mixed-state resource $\ensuremath{\Xi}$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction $\mathcal{G}[\ensuremath{\Xi}]$ and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that $\mathcal{G}[\ensuremath{\Xi}]>1∕2$. In addition, we conjecture that when $\mathcal{G}[\ensuremath{\Xi}]<1∕4$, then no entanglement could be teleported. It is shown that to determine the usefulness of $\ensuremath{\Xi}$ for E0{\mathcal{E}}_{0}E0​, it is necessary to analyze $\mathcal{G}[\ensuremath{\Xi}]$.
Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.
Mixed entangled states are generic resource for quantum teleportation. Optimal teleportation fidelity measures the success of quantum teleportation. The relevance of rank in the teleportation process is investigated by constructing three new maximally entangled mixed states (MEMS) of different ranks. Linear entropy, concurrence, optimal teleportation fidelity and Bell function are obtained for each of these states analytically. It is found that mixed states with higher rank are better resource for teleportation. In order to achieve a fixed value of optimal teleportation fidelity, we find that low rank states must have high concurrence. Further, for each of ranks 2, 3 and 4, we numerically generate 30000 maximally entangled mixed states. The analysis of these states reveals the existence of a rank dependent upper bound on optimal teleportation fidelity for a fixed purity. In order to achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a rank dependent lower bound on concurrence. MEMS are classified in terms of their degree of nonlocality. The results are found to be same with logarithmic negativity used as a measure of entanglement.
Motivated by the results of Macchiavello and Palma on entanglement-enhanced information transmission over a quantum channel with correlated noise, we demonstrate how the entanglement teleportation scheme of Lee and Kim gives rise to two uncorrelated generalized depolarizing channels. In an attempt to find a teleportation scheme that yields two correlated generalized depolarizing channels, we discover a teleportation scheme that allows one to learn about the entanglement in an entangled pure input state, without decreasing the amount of entanglement associated with it.
Abstract From the perspective of state-channel interaction, standard quantum teleportation can be viewed as a communication process characterized by both input and output, functioning as a quantum depolarizing channel. To achieve a precise quantification of the quantumness introduced by this channel, we examine its uncertainties, which encompass both state-dependent and state-independent uncertainties. Specifically, for qudit systems, we provide general formulas for these uncertainties. We analyze the uncertainties associated with standard quantum teleportation when induced by isotropic states, Werner states, and X-states, and we elucidate the correlation between these uncertainties and the parameters of the specific mixed states. Our findings demonstrate the validity of quantifying these uncertainties.
In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. If a non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1−(1− C 2 ) 1/2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation, Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.