Recently, new insights have been obtained by jointly studying classical communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we study non-signaling assisted classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. The corresponding one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its non-signaling assisted one-shot classical capacity. This finding, therefore, bridges classical communication and thermodynamics. We also apply our approach to study how many pairs of orthogonal maximal entanglement can be maintained under channels constrained by different forms of inseparability. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.
Recently, new insights have been obtained by jointly studying classical communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we study non-signaling assisted classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. The corresponding one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its non-signaling assisted one-shot classical capacity. This finding, therefore, bridges classical communication and thermodynamics. We also apply our approach to study how many pairs of orthogonal maximal entanglement can be maintained under channels constrained by different forms of inseparability. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.
Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability , which is constructed as a channel resource theory induced by a state resource theory. We provide two general classes of resource preservability monotones: One is based on state resource monotones, and another is based on channel distance measures. Specifically, the latter gives the robustness monotone, which has been recently found to have an operational interpretation. As examples, we show that athermality preservability of a Gibbs-preserving channel can be related to the smallest bath size needed to thermalize all its outputs, and it also bounds the capacity of a classical communication scenario under certain thermodynamic constraints. We further apply our theory to the study of entanglement preserving local thermalization (EPLT) and provide a new family of EPLT which admits arbitrarily small nonzero entanglement preservability and free entanglement preservation at the same time. Our results give the first systematic and general formulation of the resource preservation character of free operations.
A fundamental problem in resource theory is to study the manipulation of the resource. Focusing on a general dynamical resource theory of quantum channels, here we consider tasks of one-shot resource distillation and dilution with a single copy of the resource. For any target of unitary channel or pure state preparation channel, we establish a universal strategy to determine upper and lower bounds on rates that convert between any given resource and the target. We show that the rates are related to resource measures based on the channel robustness and the channel hypothesis testing entropy, with regularization factors of the target resource measures. The strategy becomes optimal with converged bounds when the channel robustness is finite and measures of the target resource collapse to the same value. The single-shot result also applies to asymptotic parallel manipulation of channels to obtain asymptotic resource conversion rates. We give several examples of dynamical resources, including the purity, classical capacity, quantum capacity, non-uniformity, coherence, and entanglement of quantum channels. Our results are applicable to general dynamical resource theories with potential applications in quantum communication, fault-tolerant quantum computing, and quantum thermodynamics.
For a classical channel, neither the Shannon ca-pa-city, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Yet, perhaps somewhat counterintuitively, entanglement assistance can help and actually elevate the chances of success even in a one-way communicational task that is to be completed by a single-shot use of a noiseless classical channel.To quantify the help that a non-signaling resource provides to a noiseless classical channel, one might ask how many extra letters should be added to the alphabet of the channel in order to perform equally well without the specified non-signaling resource. As was observed by Cubitt, Leung, Matthews, and Winter, there is no upper bound on the number of extra letters required for substituting the assistance of a general non-signaling resource to a noiseless one-bit classical channel. In contrast, here we prove that if this resource is a bipartite quantum system in a maximally entangled state, then an extra classical bit always suffices as a replacement.
We introduce a resource theory of channels relevant to communication via quantum channels, in which the set of constant channels-useless channels for communication tasks-are considered as free resources. We find that our theory with such a simple structure is useful to address central problems in quantum Shannon theory-in particular, we provide a converse bound for the one-shot nonsignaling assisted classical capacity that naturally leads to its strong converse property, as well as obtain the one-shot channel simulation cost with nonsignaling assistance. We clarify an intimate connection between the nonsignaling assistance and our formalism by identifying the nonsignaling assisted channel coding with the channel transformation under the maximal set of resource nongenerating superchannels, providing a physical characterization of the latter. Our results provide new perspectives and concise arguments to those problems, connecting the recently developed fields of resource theories to "classic" settings in quantum information theory and shedding light on the validity of resource theories of channels as effective tools to address practical problems.
We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglementassisted classical communication can be achieved by activated, no-signaling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the Υ-information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels, we show that the Υ-information is a strong converse bound.
Current advancements in communication equipment demand the investigation of classical information transfer over quantum channels, by encompassing realistic scenarios in finite dimensions. To address this issue, we develop a framework for analyzing classical capacities of quantum channels where the set of states used for encoding information is restricted based on various physical properties. Specifically, we provide expressions for the classical capacities of noiseless and noisy quantum channels when the average energy of the encoded ensemble or the energy of each of the constituent states in the ensemble is bounded. In the case of qubit energy-preserving dephasing channels, we demonstrate that a nonuniform probability distribution based on the energy constraint maximizes capacity, while we derive the compact form of the capacity for equiprobable messages. We suggest an energy-constrained dense coding (DC) protocol that we prove to be optimal in the two-qubit situation and obtain a closed-form expression for the DC capacity. Additionally, we demonstrate a no-go result, which states that when the dimension of the sender and the receiver is two, no energy-preserving operation can offer any quantum advantage for energy-constrained entanglement-assisted capacity. We exhibit that, in the energy-constrained situation, classical-quantum noisy channels can show improved capabilities under entanglement assistance, a phenomenon that is unattainable in the unrestricted scenario.