Abstract
More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here, we give an answer to this question for temporal processes that are probed sequentially by means of projective measurements of the same observable. Defining classical processes as those that can, in principle, be simulated by means of classical resources only, we fully characterize the set of such processes. Based on this characterization, we show that for non-Markovian processes (i.e., processes with memory), the absence of coherence does not guarantee the classicality of observed phenomena; furthermore, we derive an experimentally and computationally accessible measure for nonclassicality in the presence of memory. We then provide a direct connection between classicality and the vanishing of quantum discord between the evolving system and its environment. Finally, we demonstrate that—in contrast to the memoryless setting—in the non-Markovian case, there exist processes that are genuinely quantum; i.e., they display nonclassical statistics independent of the measurement scheme that is employed to probe them.
- Received 3 September 2019
- Revised 11 August 2020
- Accepted 10 September 2020
DOI:https://doi.org/10.1103/PhysRevX.10.041049
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Our approach is based upon the so-called Kolmogorov conditions, which form the foundation of classical stochastic processes and provide a set of experimentally testable requirements that every classical process must satisfy. Based on this, we characterize the set of all quantum processes that cannot be understood in classical terms and identify the mechanisms that lead to their nonclassicality.
While a common mathematical signifier of quantumness is the connection between nonclassicality and coherence, we prove that classicality is intimately related to quantum discord, a type of nonclassical correlation between two systems. We also show that a fundamental gap arises between processes with and without memory. For example, processes without memory can always “hide” their quantumness, while some processes with memory can never appear classical.
Our results provide a comprehensive picture of nonclassicality and firmly connect abstract, mathematical notions of quantumness with a fully operational definition. The concepts we introduce are immediately applicable to a wide array of experimental situations, such as quantum transport phenomena, where it is becoming increasingly important to assess whether or not reported advantages are actually due to quantum resources.
