SciPost Physics

SciPost Phys. 10, 141 (2021) · published 11 June 2021

• doi: 10.21468/SciPostPhys.10.6.141
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

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.

• Dowling et al., Relaxation of Multitime Statistics in Quantum Systems
  Quantum 7, 1027 1027 (2023) [Crossref]
• Burgarth et al., Quantum non-Markovianity elusive to interventions
  Phys. Rev. A 104, L050404 (2021) [Crossref]
• Capela et al., Quantum Markov monogamy inequalities
  Phys. Rev. A 106, 022218 (2022) [Crossref]
• Al Rasbi et al., Quantum physics cannot be captured by classical linear hidden variable theories even in the absence of entanglement
  Front. Phys. 12, 1325239 (2024) [Crossref]
• Figueroa-Romero et al., Operational Markovianization in randomized benchmarking
  Quantum Sci. Technol. 9, 035020 (2024) [Crossref]
• Milz et al., Resource theory of causal connection
  Quantum 6, 788 788 (2022) [Crossref]
• Dowling et al., Equilibration of multitime quantum processes in finite time intervals
  SciPost Phys. Core 6, 043 (2023) [Crossref]
• Milz et al., Quantum Stochastic Processes and Quantum non-Markovian Phenomena
  PRX Quantum 2, 030201 (2021) [Crossref]
• Berk et al., Extracting quantum dynamical resources: consumption of non-Markovianity for noise reduction
  npj Quantum Inf 9, 104 (2023) [Crossref]
• Figueroa-Romero et al., Randomized Benchmarking for Non-Markovian Noise
  PRX Quantum 2, 040351 (2021) [Crossref]
• Aloisio et al., Sampling Complexity of Open Quantum Systems
  PRX Quantum 4, 020310 (2023) [Crossref]
• Figueroa-Romero et al., Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
  Quantum 6, 868 868 (2022) [Crossref]
• Gribben et al., Exact Dynamics of Nonadditive Environments in Non-Markovian Open Quantum Systems
  PRX Quantum 3, 010321 (2022) [Crossref]
• Kalaga et al., Legget-Garg inequality for a two-mode entangled bosonic system
  Opt. Express 32, 9946 (2024) [Crossref]
• Zambon et al., Relations between Markovian and non-Markovian correlations in multitime quantum processes
  Phys. Rev. A 109, 062401 (2024) [Crossref]
• Zambon, Process tensor distinguishability measures
  Phys. Rev. A 110, 042210 (2024) [Crossref]
• Taranto et al., Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
  Quantum 8, 1328 1328 (2024) [Crossref]
• Dowling et al., Capturing Long-Range Memory Structures with Tree-Geometry Process Tensors
  Phys. Rev. X 14, 041018 (2024) [Crossref]
• Dowling et al., Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal-Entanglement Structure
  PRX Quantum 5, 010314 (2024) [Crossref]
• Nery et al., Simple and maximally robust processes with no classical common-cause or direct-cause explanation
  Quantum 5, 538 538 (2021) [Crossref]