arXiv:2212.04876 · Journal of Physics A Mathematical and Theoretical

Adjusting phase-covariant qubit channel performance with non-unitality

Katarzyna Siudzińska, Michał Studziński

Published Apr 13, 2023• 5 citations

Abstract

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.

DOI: 10.1088/1751-8121/acccbf

Related papers

Improving classical capacity of qubit dynamical maps through stationary state manipulation

Katarzyna Siudzińska

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.

arXiv:2302.11519Journal of Physics A Mathematical and TheoreticalMay 2, 20231 citation

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:2206.10742Journal of Physics A Mathematical and TheoreticalSep 8, 20226 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:2210.17448Journal of Physics CommunicationsJun 24, 20233 citations

Characterizing qubit channels in the context of quantum teleportation

Arkaprabha Ghosal, Debarshi Das, Subhashish Banerjee

We consider a scenario where a party, say, Alice prepares a pure two-qubit (either maximally entangled or nonmaximally entangled) state and sends one half of this state to another distant party, say, Bob through a qubit (either unital or nonunital) channel. Finally, the shared state is used as a teleportation channel. In this scenario, we focus on characterizing the set of qubit channels with respect to the final state's efficacy as a resource of quantum teleportation (QT) in terms of maximal average fidelity and fidelity deviation (fluctuation in fidelity values over the input states). Importantly, we point out the existence of a subset of qubit channels for which the final state becomes useful for universal QT (having maximal average fidelity strictly greater than the classical bound and having zero fidelity deviation) when the initially prepared state is either useful for universal QT (i.e., for a maximally entangled state) or not useful for universal QT (i.e., for a subset of nonmaximally entangled pure states). Interestingly, in the latter case, we show that nonunital channels (dissipative interactions) are more effective than unital channels (nondissipative interactions) in producing useful states for universal QT from nonmaximally entangled pure states.

arXiv:2102.02054Physical Review AMay 18, 202111 citations

Properties of Conjugate Channels with Applications to Additivity and Multiplicativity

Christopher King, Keiji Matsumoto, Michael Nathanson +1 more

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the conjugate channel. We explore the properties of conjugate channels and describe several different methods of construction. In general, conjugate channels map M_d to M_d' with d < d', and different constructions may differ by conjugation with a partial isometry. We show that a channel and its conjugate have the same minimal output entropy and maximal output p-norm. It then follows that the additivity and multiplicativity conjectures for these measures of optimal output purity hold for a product of channels if and only if they also hold for the product of their conjugates. This allows us to reduce these conjectures to the special case of maps taking M_d to M_d' with a minimal representation of dimension at most d. We find explicit expressions for the conjugates for a number of well-known examples, including entanglement-breaking channels, unital qubit channels, the depolarizing channel, and a subclass of random unitary channels. For the entanglement-breaking channels, channels this yields a new class of channels for which additivity and multiplicativity of optimal output purity can be established. For random unitary channels using the generalized Pauli matrices, we obtain a new formulation of the multiplicativity conjecture. The conjugate of the completely noisy channel plays a special role and suggests a mechanism for using noise to transmit information.

arXiv:quant-ph/0509126Markov Processes And Related FieldsSep 19, 2005115 citations

Non-locality breaking qubit channels

Rajarshi Pal, Sibasish Ghosh A

Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breaking such a property does not hold in general, though for certain channels and for a restricted class of states for all channels this holds.We also consider channels whose output remains local under SLOCC and call them `strongly non-locality breaking'. We provide a closed form necessary-sufficient condition for any two-qubit state to show hidden CHSH nonlocality, which is likely to be useful for other purposes as well. This in turn allows us to characterize all strongly non-locality breaking qubit channels. It turns out that unital qubit channels breaking nonlocality of maximally entangled states are strongly non-locality breaking while extremal qubit channels cannot be so unless they are entanglement breaking.

arXiv:1306.3151Jun 13, 20130 citations