Seonglae ChoQuantum State Over Time
QSOT is a spacetime density-matrix concept that tries to express "what state a quantum system was in across time" as if it were a joint quantum state. In other words, it is a framework for capturing not the quantum state at a single instant, but the states of a quantum system at several times together with their temporal correlations, all as a single mathematical object.
In ordinary quantum mechanics, the state at a particular time is written as a density matrix , and the time evolution is described separately by a quantum channel . QSOT merges the two into roughly
so that "the state at time A" plus "the dynamics from A to B" become a single joint operator. Taking the marginals of this object must recover the original initial state and final state respectively.
That is, the idea is to treat temporal correlations the way we treat spatial correlations. However, because the past and the future are not independent subsystems, QSOT is not exactly the same as an ordinary density matrix, and it need not be positive semidefinite. Recent work has connected QSOT to temporal correlations that are measurable via interferometry, non-Markovian dynamics, and related topics. A 2026 PRL paper also treats the conventional density operator, QSOT, and the process matrix in a unified way.