We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated preprocessing and postprocessing maps only.Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels).These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially).As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non-entanglement-breaking channel can be certified.Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification.As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted.An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.
We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated preprocessing and postprocessing maps only.Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels).These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially).As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non-entanglement-breaking channel can be certified.Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification.As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted.An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.
Entanglement-breaking channels (equivalently, measure-and-prepare channels) are quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been widely employed in defining notions of “classical memory,” under the assumption that such channels effectively act as a classical resource. In this paper, we show that this assumption is false. By means of multitime correlations, we conclusively show that entanglement-breaking channels are still a quantum resource: A qudit going through an entanglement-breaking channel can generate genuinely nonclassical temporal correlations, i.e., that cannot be simulated by a classical system of same dimension. Our results imply that entanglement-breaking channels cannot generally be employed to characterize classical memory effects without additional assumptions.
Abstract A proper quantum memory is argued to consist in a quantum channel which cannot be simulated with a measurement followed by classical information storage and a final state preparation, i.e. with an entanglement breaking (EB) channel. The verification of quantum memories (non-EB channels) is a task in which an honest user wants to test the quantum memory of an untrusted, remote provider. This task is inherently suited for the class of protocols with trusted quantum inputs, sometimes called measurement-device-independent (MDI) protocols. Here, we study the MDI certification of non-EB channels in continuous variable (CV) systems. We provide a simple witness based on adversarial metrology, and describe an experimentally friendly protocol that can be used to verify all non Gaussian incompatibility breaking quantum memories. Our results can be tested with current technology and can be applied to test other devices resulting in non-EB channels, such as CV quantum transducers and transmission lines.
High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking channels (non-NPT-breaking channels). Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.
We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a modification of conditional min-entropies, with respect to the set F of allowed transformations, and show that under some conditions on F, these quantities characterize approximate simulability. If F is the set of free superchannels in a quantum resource theory of processes, the modified conditional min-entropies form a complete set of resource monotones. If the transformations in F consist of a preprocessing and a postprocessing of specified forms, approximate simulability is also characterized in terms of success probabilities in certain guessing games, where a preprocessing of a given form can be chosen and the measurements are restricted. These results are applied to several specific cases of simulability of quantum channels, including postprocessings, preprocessings and processing of bipartite channels by LOCC superchannels and by partial superchannels, as well as simulability of sets of quantum measurements. These questions are first studied in a general setting that is an extension of the framework of general probabilistic theories (GPT), suitable for dealing with channels. Here we prove a general theorem that shows that approximate simulability can be characterized by comparing outcome probabilities in certain tests. This result is inspired by the classical Le Cam randomization criterion for statistical experiments and contains its finite dimensional version as a special case.
Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for any quantum technology to exhibit operational advantage. There is thus great value in identifying physically meaningful means to benchmark candidate quantum memories against each other across diverse operational settings. Here we introduce the robustness of quantum memory, and prove that it satisfies all the mathematical properties we expect of a bona-fide resource-theoretic measure of a system's capacity to retain non-classical information. We demonstrate its operational meaning as a resource in three different settings: (1) the resource cost of synthesising the memory with idealised qubit memories, (2) the resource cost of simulating the memory's observational statistics with classical resources, and (3) the performance of the memory in discriminating different input states. We illustrate an efficient semi-definite program to estimate the robustness of quantum memory, and show that it can be lower bounded with a single witness or purity measurement. Our results thus provide an experimentally accessible and operationally meaningful quantifier of the resources behind preserving quantum information.
While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.