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

IEEE Transactions on Information Theory

Quantum signal propagation in depolarizing channels

Nicholas J. Pippenger

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Let X be an unbiased random bit, let Y be a qubit. whose mixed state depends on X, and let the qubit Z be the result of passing Y through a depolarizing channel, which replaces Y with a completely random qubit with probability p. We measure the quantum mutual information between X and Y by T(X; Y)=S(X)+S(Y)-S(X, Y), where S(...) denotes von Neumann's (1948) entropy. (Since X is a classical bit, the quantity T(X; Y) agrees with Holevo's (1973) bound /spl chi/(X; Y) to the classical mutual information between X and the outcome of any measurement of Y.) We show that T(X; Z) /spl les/ (1-p)/sup 2/T(X; Y). This generalizes an analogous bound for classical mutual information due to Evans and Schulman (1993), and provides a new proof of their result.

DOI
10.1109/18.971755

Related papers

The capacity of the quantum depolarizing channel

Christopher King

The information-carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measurements give any advantage for information capacity. The result follows from an additivity theorem for the product channel /spl Delta//spl ominus//spl Psi/, where /spl Delta/ is the depolarizing channel and /spl Psi/ is a completely arbitrary channel. We establish the Amosov-Holevo-Werner(see Probl. Inform. Transm., vol.36, p.305-313, 2000) p-norm conjecture for this product channel for all p/spl ges/1, and deduce from this the additivity of the minimal entropy and of the Holevo quantity /spl chi//sup */.

arXiv:quant-ph/0204172•IEEE Transactions on Information Theory•Jan 1, 2003•290 citations

von Neumann capacity of noisy quantum channels

Christoph Adami, Nicolas J. Cerf

We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the ``Kholevo capacity'') when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.

arXiv:quant-ph/9609024•Physical Review A•Nov 1, 1997•209 citations

Lower Bound for Mutual Information of a Quantum Channel

Horia Scutaru

We obtain a lower bound for the mutual information of a quantum transmission channel, which is perfectly analogous with Holevo's upper bound. The Uhlmann inequality for relative entropies is used, in a reverted order, for a completely positive mapping related with the mixed coherent states introduced by us seventeen years ago. Possible applications to quantum cryptography are discussed.

Physical Review Letters•Jul 31, 1995•9 citations

Strictly discordant quantum probes of the qubit depolarizing channel

Michael R. Frey, Theodore J. Yoder

Quantum mutual information defined in terms of von Neumann entropy captures and quantifies all correlations, quantum and classical, between the two parts of a bipartite quantum system. Within this framework entanglement is the most distinguished type of quantum correlation, and a rich body of theory and experiment establishes that entanglement is a potent and fungible resource for quantum information processing broadly. Bipartite systems can exhibit quantum correlations beyond entanglement. Such non-classical states are called discordant in general and strictly discordant (or dissonant) when the quantum state is separable. We show that strict discord can increase the amount of information available from probing a quantum channel. We focus in this study on the qubit depolarizing channel, using quantum Fisher information to measure the information available about the channel depolarizing probability. We consider channel probes prepared, along with an ancilla, in a separable two-qubit Bell-diagonal state. We prove for Bell-diagonal probes of the qubit depolarizing channel that, in the absence of entanglement and controlling for marginal purity and degree of classical correlation, any increase in strict discord between the probe and ancilla yields an accompanying increase in available statistical information about the channel depolarizing probability.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 2012•0 citations

Relating Entropies of Quantum Channels

Dariusz Kurzyk, Łukasz Pawela, Zbigniew Puchała

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

arXiv:2106.09629•Entropy•Aug 10, 2021•3 citations

Quantum entanglement and classical communication through a depolarizing channel

Dagmar Bruß, Lara Faoro, Chiara Macchiavello +1 more

We analyse the role of entanglement for transmission of classical information through a memoryless depolarizing channel. Using the isotropic character of this channel we prove analytically that the mutual information cannot be increased by encoding classical bits into entangled states of two qubits.

arXiv:quant-ph/9903033•Journal of Modern Optics•Feb 1, 2000•59 citations
Let X be an unbiased random bit, let Y be a qubit. whose mixed state depends on X, and let the qubit Z be the result of passing Y through a depolarizing channel, which replaces Y with a completely random qubit with probability p. We measure the quantum mutual information between X and Y by T(X; Y)=S(X)+S(Y)-S(X, Y), where S(...) denotes von Neumann's (1948) entropy. (Since X is a classical bit, the quantity T(X; Y) agrees with Holevo's (1973) bound /spl chi/(X; Y) to the classical mutual information between X and the outcome of any measurement of Y.) We show that T(X; Z) /spl les/ (1-p)/sup 2/T(X; Y). This generalizes an analogous bound for classical mutual information due to Evans and Schulman (1993), and provides a new proof of their result.
The information-carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measurements give any advantage for information capacity. The result follows from an additivity theorem for the product channel /spl Delta//spl ominus//spl Psi/, where /spl Delta/ is the depolarizing channel and /spl Psi/ is a completely arbitrary channel. We establish the Amosov-Holevo-Werner(see Probl. Inform. Transm., vol.36, p.305-313, 2000) p-norm conjecture for this product channel for all p/spl ges/1, and deduce from this the additivity of the minimal entropy and of the Holevo quantity /spl chi//sup */.
We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the ``Kholevo capacity'') when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.
Quantum mutual information defined in terms of von Neumann entropy captures and quantifies all correlations, quantum and classical, between the two parts of a bipartite quantum system. Within this framework entanglement is the most distinguished type of quantum correlation, and a rich body of theory and experiment establishes that entanglement is a potent and fungible resource for quantum information processing broadly. Bipartite systems can exhibit quantum correlations beyond entanglement. Such non-classical states are called discordant in general and strictly discordant (or dissonant) when the quantum state is separable. We show that strict discord can increase the amount of information available from probing a quantum channel. We focus in this study on the qubit depolarizing channel, using quantum Fisher information to measure the information available about the channel depolarizing probability. We consider channel probes prepared, along with an ancilla, in a separable two-qubit Bell-diagonal state. We prove for Bell-diagonal probes of the qubit depolarizing channel that, in the absence of entanglement and controlling for marginal purity and degree of classical correlation, any increase in strict discord between the probe and ancilla yields an accompanying increase in available statistical information about the channel depolarizing probability.
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.