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arXiv:2105.12060 · Physical Review A

Creating and destroying coherence with quantum channels

Masaya Takahashi, Swapan Rana, Alexander Streltsov

Published Jun 9, 2022• 15 citations
arXivHTMLPDF

Abstract

The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this Letter we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on a multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of the coherence generating capacity of quantum channels, which we also discuss.

DOI
10.1103/physreva.105.l060401

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The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this Letter we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on a multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of the coherence generating capacity of quantum channels, which we also discuss.
Abstract Quantum coherence is a fundamental property of quantum systems that can be studied within the framework of a quantum resource theory. From this resource-theoretic approach, many similarities emerge between coherence and quantum entanglement, the latter being another prominent quantum resource. In this paper, we study the relationship between coherence and entanglement from the perspective of resource loss/gain by unitary dynamics. Specifically we consider how much coherence can be either generated or destroyed on a bipartite system when the action is restricted to local unitary (LU) operations. For pure states, we find that the relative entropy of entanglement and the robustness of entanglement provide tight lower bounds on the amount of coherence that can be destroyed by LUs, as measured by the relative entropy and measures of coherence, respectively. This provides new operational interpretations of the entanglement entropy and robustness of entanglement in pure states as the minimal amount of coherence that persists when the system is subjected to LU transformations. We then study the amount of bipartite pure entanglement that can be either maximized or minimized when the action is restricted to a global incoherent operation. For two-qubit pure states, maximum and minimum are shown in terms of coefficients of given state with incoherent basis. Finally we consider a generalized version of the recently introduced CCP of a quantum channel.
We introduce and investigate a family of entanglement-annihilating channels. These channels are capable of destroying any quantum entanglement within the system they act on. We show that they are not necessarily entanglement breaking. In order to achieve this result we analyze the subset of locally entanglement-annihilating channels. In this case, the same local noise applied on each subsystem individually is less entanglement annihilating (with respect to multi-partite entanglement) as the number of subsystems is increasing. Therefore, the bipartite case provides restrictions on the set of local entanglement-annihilating channels for the multipartite case. The introduced concepts are illustrated on the family of single-qubit depolarizing channels.
We generalize the recently proposed resource theory of coherence (or superposition) [T. Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014); A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 (2016)] to the setting where not just the free (``incoherent'') resources, but also the manipulated objects, are quantum operations rather than states. In particular, we discuss an information theoretic notion of the coherence capacity of a quantum channel and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel and prove achievability results for unitaries and general channels acting on a ddd-dimensional system; we show that a maximally coherent state of rank ddd is always sufficient as a resource if incoherent operations are allowed, and one of rank d2{d}^{2}d2 for ``strictly incoherent'' operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e., maps with nonzero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.
The study and control of coherence in quantum systems is one of the most exciting recent developments in physics. Quantum coherence plays a crucial role in emerging quantum technologies as well as fundamental experiments. A major obstacle to the utilization of quantum effects is decoherence, primarily in the form of dephasing that destroys quantum coherence, and leads to effective classical behavior. We show that there are universal relationships governing dephasing that constrain the relative rates at which quantum correlations can disappear. These lead effectively to speed limits which become especially important in multipartite systems.
Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.
Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent to which quantum coherence is diminished depends both on the channel and the incoherent basis. Motivated by this, we propose a measure of nonclassicality of a quantum channel as the average quantum coherence of the state space after the channel acts on, minimized over all orthonormal basis sets of the state space. Utilizing the squared l1{l}_{1}l1​-norm of coherence for the qubit channels, the minimization can be treated analytically and the proposed measure takes a closed form of expression. If we allow the channels to act locally on a maximally entangled state, the quantum correlation is diminished making the states more classical. We show that the extent to which quantum correlation is preserved under local action of the channel cannot exceed the quantumness of the underlying channel. We further apply our measure to the quantum teleportation protocol and show that a nonzero quantumness for the underlying channel provides a necessary condition to overcome the best classical protocols.