Quantum States Over Time: From Foundations To Applications

In this talk, I will introduce quantum states over time (QSOT), a formalism for describing quantum systems over space-time. I will begin by reviewing how QSOT has emerged in the literature. While conventional density operator formalism has been effective across many areas of quantum information theory, QSOT was developed to meet more specialized research needs— most notably, as a key ingredient to develop a quantum version of Bayes’ theorem. I will end the first part of my talk by comparing various QSOT that have been proposed.

In the second part, I will discuss the causal compatibility problem as an application of QSOT. I will focus on the temporal compatibility problem, which asks the following: from correlations in measurement outcomes alone, can two otherwise isolated parties establish whether such correlations are atemporal (i.e., temporally incompatible)? That is, can they rule out that they have been given the same system at two different times? I will first explain how characterizing measurement statistics in a causal agnostic scenario is equivalent to characterizing a specific type of QSOT, known as pseudo-density operators. I will then present our recent findings obtained by analyzing pseudo-density operators; In particular, we demonstrate that atemporality is distinct from entanglement, though they appear to be equivalent at first glance. Specifically, we show atemporality implies entanglement, but not vice versa, thus revealing that atemporality is a strictly stronger form of quantum correlations than entanglement. Nevertheless, we also find that sufficiently strong entanglement does imply atemporality.