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arXiv:1710.01776 · Physical Review A

Unifying framework for spatial and temporal quantum correlations

Fabio Costa, Martin Ringbauer, M. E. Goggin, Andrew G. White, Alessandro Fedrizzi

Published Jul 26, 2018• 32 citations
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Abstract

Measurements on a single quantum system at different times reveal rich nonclassical correlations similar to those observed in spatially separated multipartite systems. Here we introduce a theory framework that unifies the description of temporal, spatial, and spatiotemporal resources for quantum correlations. We identify and experimentally demonstrate simple cases where an exact mapping between the domains is possible. We then identify correlation resources in arbitrary situations, where not all spatial quantum states correspond to a process and not all temporal measurements have a spatial analog. These results provide a starting point for the systematic exploration of multipoint temporal correlations as a powerful resource for quantum information processing.

DOI
10.1103/physreva.98.012328

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Abstract Multipartite quantum correlations are a powerful resource that underpins applications from quantum metrology to quantum computing. While most research has focused on spatial correlations, it is now becoming clear that a sequence of measurements on a single quantum system at different points in time reveals a similarly rich, yet fundamentally different structure of multipartite temporal correlations. Here we experimentally observe genuine multi-time correlations in a sequence of three generalized measurements on a single photon. These correlations, manifest by a simultaneous violation of all pairwise Bell inequalities, cannot be reproduced by any spatial quantum state of equal dimension. Our work lays the foundation for the exploration of temporal correlations arising in quantum networks for quantum information applications.
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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.
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