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:2302.11519 · Journal of Physics A Mathematical and Theoretical

Improving classical capacity of qubit dynamical maps through stationary state manipulation

Katarzyna Siudzińska

Published May 2, 2023• 1 citation
arXivHTMLPDF

Abstract

Abstract We analyze the evolution of Holevo and entanglement-assisted classical capacities for two classes of phase-covariant channels. In particular, we show that these capacities can be improved by changing the stationary state of the channel, which is closely related to its non-unitality degree. The more non-unital the channel, the greater its capacity. The channel parameters are engineered through mixtures on the level of dynamical maps, time-local generators, and memory kernels, for which we propose construction methods. For highly non-unital maps, we achieve a temporary increase in the classical capacity that exceeds the entanglement-assisted classical capacity of the unital map. This shows that non-unitality can become a better quantum resource for information transition purposes than quantum entanglement.

DOI
10.1088/1751-8121/acd1c7

Related papers

Adjusting phase-covariant qubit channel performance with non-unitality

Katarzyna Siudzińska, Michał Studziński

Abstract We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for the minimal and maximal channel fidelity on pure states and maximal output purity. Next, we introduce a measure of non-unitality and show how to manipulate between unital and maximally non-unital maps by considering classical mixtures of quantum channels. Finally, we prove that maximal fidelity and maximal output purity increase with non-unitality and present several examples. Interestingly, non-unitality can also prolong quantum entanglement and lead to its rebirth.

arXiv:2212.04876•Journal of Physics A Mathematical and Theoretical•Apr 13, 2023•5 citations

Geometry of phase-covariant qubit channels

Katarzyna Siudzińska

Abstract We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamiołkowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the parameter that characterizes non-unitality. We find the shapes and analytically compute the volumes of phase-covariant channels, in particular entanglement breaking and obtainable with time-local generators.

arXiv:2210.17448•Journal of Physics Communications•Jun 24, 2023•3 citations

Classical and entanglement-assisted capacity of a qubit depolarizing memory channel

Jaideep Mulherkar

We study the classical and entanglement-assisted capacity of a forgetful quantum memory channel that randomly switches between two qubit depolarizing channels. We show that when the input consists of two qubits then depending on channel parameters either the maximally entangled input states or product input states achieve the two-use classical capacity. We conjecture that as the number of input qubits is increased the classical capacity approaches the product state capacity for all values of the parameters. We also derive an expression for the entanglement-assisted classical capacity of this quantum memory channel in terms of the entropy rate of a Markov chain.

arXiv:1503.07075•International Journal of Quantum Information•Apr 1, 2016•3 citations

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

Katarzyna Siudzińska, Arpan Das, Anindita Bera

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.

arXiv:2109.10152•Entropy•Oct 21, 2021•6 citations

Beware of Greeks bearing entanglement? Quantum covert channels, information flow and non-local games

David Mestel

Can quantum entanglement increase the capacity of (classical) covert channels? To one familiar with Holevo's Theorem it is tempting to think that the answer is obviously no. However, in this work we show: quantum entanglement can in fact increase the capacity of a classical covert channel, in the presence of an active adversary; on the other hand, a zero-capacity channel is not improved by entanglement, so entanglement cannot create ‘purely quantum’ covert channels; the problem of determining the capacity of a given channel in the presence of entanglement is undecidable; but there is an algorithm to bound the entangled capacity of a channel from above, adapted from the semi-definite hierarchy from the theory of non-local games, whose close connection to channel capacity is at the core of all of our results.

arXiv:2202.02069•IEEE Computer Security Foundations Workshop (CSFW)•Aug 1, 2022•0 citations

Phase-covariant mixtures of non-unital qubit maps

Katarzyna Siudzińska

Abstract We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital channels can result in restoring the unitality, whereas mixing commutative maps can lead to non-commutativity. For the convex combinations of Markovian semigroups, we prove that classical uncertainties cannot break quantum Markovianity. Moreover, contrary to the Pauli channel case, the semigroup can be recovered only by mixing two other semigroups.

arXiv:2206.10742•Journal of Physics A Mathematical and Theoretical•Sep 8, 2022•6 citations
Abstract We analyze the evolution of Holevo and entanglement-assisted classical capacities for two classes of phase-covariant channels. In particular, we show that these capacities can be improved by changing the stationary state of the channel, which is closely related to its non-unitality degree. The more non-unital the channel, the greater its capacity. The channel parameters are engineered through mixtures on the level of dynamical maps, time-local generators, and memory kernels, for which we propose construction methods. For highly non-unital maps, we achieve a temporary increase in the classical capacity that exceeds the entanglement-assisted classical capacity of the unital map. This shows that non-unitality can become a better quantum resource for information transition purposes than quantum entanglement.
Abstract We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for the minimal and maximal channel fidelity on pure states and maximal output purity. Next, we introduce a measure of non-unitality and show how to manipulate between unital and maximally non-unital maps by considering classical mixtures of quantum channels. Finally, we prove that maximal fidelity and maximal output purity increase with non-unitality and present several examples. Interestingly, non-unitality can also prolong quantum entanglement and lead to its rebirth.
We study the classical and entanglement-assisted capacity of a forgetful quantum memory channel that randomly switches between two qubit depolarizing channels. We show that when the input consists of two qubits then depending on channel parameters either the maximally entangled input states or product input states achieve the two-use classical capacity. We conjecture that as the number of input qubits is increased the classical capacity approaches the product state capacity for all values of the parameters. We also derive an expression for the entanglement-assisted classical capacity of this quantum memory channel in terms of the entropy rate of a Markov chain.
Can quantum entanglement increase the capacity of (classical) covert channels? To one familiar with Holevo's Theorem it is tempting to think that the answer is obviously no. However, in this work we show: quantum entanglement can in fact increase the capacity of a classical covert channel, in the presence of an active adversary; on the other hand, a zero-capacity channel is not improved by entanglement, so entanglement cannot create ‘purely quantum’ covert channels; the problem of determining the capacity of a given channel in the presence of entanglement is undecidable; but there is an algorithm to bound the entangled capacity of a channel from above, adapted from the semi-definite hierarchy from the theory of non-local games, whose close connection to channel capacity is at the core of all of our results.
Abstract We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital channels can result in restoring the unitality, whereas mixing commutative maps can lead to non-commutativity. For the convex combinations of Markovian semigroups, we prove that classical uncertainties cannot break quantum Markovianity. Moreover, contrary to the Pauli channel case, the semigroup can be recovered only by mixing two other semigroups.