We quantify in a unified approach the nonlocal resources of bipartite quantum channels and identify their component resisting the effects of dephasing noise. Despite its classical nature, we demonstrate that the latter plays a relevant role in performing quantum protocols, such as state transformations and quantum coding for noisy communication. When comparing different resource types, we show that simulating certain stochastic processes with quantum channels has a communication advantage with respect to their classical simulation, even when dephasing noise occurs. This approach also allows us to lower bound the amount of shared entanglement and communication needed to simulate bipartite quantum channels and to inner approximate the set of n-round local operations, assisted with classical communication.
We quantify in a unified approach the nonlocal resources of bipartite quantum channels and identify their component resisting the effects of dephasing noise. Despite its classical nature, we demonstrate that the latter plays a relevant role in performing quantum protocols, such as state transformations and quantum coding for noisy communication. When comparing different resource types, we show that simulating certain stochastic processes with quantum channels has a communication advantage with respect to their classical simulation, even when dephasing noise occurs. This approach also allows us to lower bound the amount of shared entanglement and communication needed to simulate bipartite quantum channels and to inner approximate the set of n-round local operations, assisted with classical communication.
Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we develop a dynamical framework in which quantum Bell nonlocality emerges as a special form of entanglement and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of classical and quantum processes, which are defined as channels that map elements between specific intervals in space and time. Entanglement is identified as a process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input-to-output delay time. LOCC preprocessing is a natural set of free operations in this theory, thereby providing previous nonlocality activation results a clear resource-theoretic foundation. We provide a systematic method to quantify the Bell nonlocality of a bipartite quantum channel. It is shown that both the relative entropy and the max relative entropy of nonlocality are nonadditive for a family of bipartite classical channels. This family includes the channel obtained when using the singlet state to maximally violate the CHSH inequality. We also find that the regularized relative entropy of Bell nonlocality provides an upper bound on the asymptotic rate of converting (i.e., simulating) many copies of one classical instantaneous resource to another.
Certifying quantum properties from the probability distributions they induce is an important task for several purposes. While this framework has been largely explored and used for quantum states, its extrapolation to the level of channels started recently in a variety of approaches. In particular, little is known about to what extent noise can spoil certification methods for channels. In this work we provide a unified methodology to certify nonlocal properties of quantum channels from the correlations obtained in prepare-and-measurement protocols: our approach gathers fully and semi-device-independent existing methods for this purpose, and extends them to new certification criteria. In addition, the effect of different models of dephasing noise is analysed. Some noise models are shown to generate nonlocality and entanglement in special cases. In the extreme case of complete dephasing, the measurement protocols discussed yield particularly simple tests to certify nonlocality, which can be obtained from known criteria by fixing the dephasing basis. These are based on the relations between bipartite quantum channels and their classical analogues: bipartite stochastic matrices defining conditional distributions.
Abstract Can quantum processes be simulated using only classical resources? This question delineates the boundary between classical and quantum models and clarifies the origin of quantum advantage in information processing. We address this question through the task of quantum channel simulation, where a sender (Alice) holds the classical description of a quantum state and wishes to transmit it to a receiver (Bob) for measurement. Prior work has shown that, for qubit channels, 2 bits of forward communication with shared randomness suffice to reproduce the statistics of any single-qubit measurement. We argue, however, that true channel simulation requires reproducing statistics of joint measurements—including entangled effects—on Alice’s state and an auxiliary system held by Bob. Such scenarios naturally arise in network communication, where some nodes know the state, while others do not. We prove that a perfect qubit channel cannot be simulated with any finite amount of classical communication, even using the most general multi-round, bidirectional protocols. We further show that this no-go result is rooted in the necessity of reproducing statistics associated with entangled effects. On the other hand, we show that noisy qubit channels, such as depolarizing channels, admit classical simulation, though the required communication diverges as noise decreases.
Quantum mechanics is a highly nonlocal theory of nature. Quantum systems exhibit correlations which cannot be described by any classical theory of locality. We develop the resource theory of dynamical Bell nonlocality, which includes bipartite states, classical channels, quantum channels and measurements. In the state scenario, all separable states are Bell local. However, there exist mixed bipartite entangled states which also admit Bell local behaviour. To address this anomaly, we introduce the notion of fully Bell locality and show that all entangled states are Bell nonlocal, in the sense that they can be used to simulate at least one nonlocal bipartite Positive Operator Valued Measure (POVM) channel. We take a step further and generalise this result to bipartite entangled quantum channels. We then generalize the CHSH inequality from bipartite classical channels to bipartite POVM channels and devise a technique to check if a given bipartite POVM channel is nonlocal or not. Finally we provide a systematic method to quantify Bell nonlocality of bipartite quantum channels by extending any monotone for Bell nonlocality of classical channels to quantum channels and also introduce the precise definition of relative entropy of Bell nonlocality. We leave some open problems in the way.
Nonlocality is at the heart of quantum information processing. In this paper we investigate the minimum amount of classical communication required to simulate a nonlocal quantum measurement. We derive general upper bounds, which in turn translate to systematic classical simulations of quantum communication protocols.As a concrete application, we prove that any quantum communication protocol with shared entanglement for computing a Boolean function can be simulated by a classical protocol whose cost does not depend on the amount of the shared entanglement. This implies that if the cost of communication is a constant, quantum and classical protocols, with shared entanglement and shared coins, respectively, compute the same class of functions.Furthermore, we describe a new class of efficient quantum communication protocols based on fast quantum algorithms. While some of them have efficient classical simulations by our method, others appear to be good candidates for separating quantum v.s. classical protocols, and quantum protocols with v.s. without shared entanglement.Yet another application is in the context of simulating quantum correlations using local hidden variable models augmented with classical communications. We give a constant cost, approximate simulation of quantum correlations when the number of correlated variables is a constant, while the dimension of the entanglement and the number of possible measurements can be arbitrary.Our upper bounds are expressed in terms of some tensor norms on the measurement operator. Those norms capture the nonlocality of bipartite operators in their own way and may be of independent interest and further applications.
This thesis takes a deep dive into quantum resources and their applications for quantum networks. In particular, this work reviews the concept of quantum correlations beyond entanglement and introduces a method for deterministically creating them via local operations by using classical correlations as a resource. The structure of these states is analysed in multipartite quantum networks, highlighting their generally asymmetric nature. We then explore how these quantum correlations can be used for entanglement generation protocols themselves and compare them to directly distributing a maximally entangled state through noisy channels. We find that, in certain noise regimes, these protocols can indeed outperform direct entanglement distribution, provided the memories at each node are sufficiently maintained. The application of multipartite quantum teleportation to multiple receivers in a network is also assessed, exploring the necessary and sufficient resources to ensure that the performance of quantum telecloning surpasses that of all known methods involving only classical communication. Our results show that, despite the genuine multipartite entanglement present in the resource state, only a few bipartite entanglement pairings are necessary for such a feat. This allows for a potential reduction in resource consumption for future experimental implementations. Thesis is embargoed until 31 December 2026.