Abstract
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 pre/post processing 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.
Highlights
Consider a vendor selling quantum devices purportedly able to store quantum information for a period of time
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
We provide a resource theory necessary to distinguishentanglement-breaking quantum channels as different classes of resources, mirroring the resource theory of entangled states and their transformations under LOCC
Summary
Consider a vendor selling quantum devices purportedly able to store quantum information for a period of time. The violation of any Bell inequality between R and B would constitute irrefutable evidence that the state φ RB is entangled and that the channel N is in the quantum domain, even in the case in which both preparation and measurement devices are untrusted This approach allows one to verify a quantum channel in a fully device-independent way, namely, based solely on the correlations observed in the experiment. We will work within the so-called measurement device-independent (MDI) framework [39], in particular, taking inspiration from semiquantum nonlocal games [40], which generalize the usual Bell-nonlocal games by enabling the referee to send quantum input states to the players Until now, this framework has only been applied to scenarios involving spacelike separated systems, where all entangled states can be detected [39,40]; this characterization is faithful even in the presence of arbitrary losses [34] and classical communication between the systems [41]. We apply the MDI framework to temporal correlations arising out of the use of a quantum memory
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