Quantum operations with the time axis in a superposed direction

TL;DR

This paper introduces a generalized transposition framework for quantum operations that allows the time axis to be in a superposed state, extending the concept of indefinite causal order and exploring implications for quantum gravity and causality.

Contribution

It proposes a new generalized transposition method that enables superposition of time directions in quantum processes, broadening the understanding of temporal symmetries in quantum mechanics.

Findings

Superposition of time axes reduces information exchange to prevent causality violations.

Generalized transposition applies to continuous perfect tensors and bipartite quantum interactions.

Framework may inform approaches where space and time are treated equally, like quantum gravity.

Abstract

In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examining if it remains physical. However, recent discoveries regarding the indefinite causal order of quantum processes suggest that there may be other, more general symmetry transformations of time besides the complete reversal. In this work, we introduce an expanded concept of matrix transposition, the generalized transposition, that takes into account general bipartite unitary transformations of a quantum operation's future and past Hilbert spaces, allowing for making the time axis definitely lie in a superposed direction, which generalizes the previously studied `indefinite direction of time', i.e., superposition of the forward and the backward time evolution. This framework may have applications in approaches that treat time and space equally like quantum gravity, where the spatio-temporal structure is explained to emerge from quantum mechanics. We apply this generalized transposition to investigate a continuous generalization of perfect tensors, a dynamic version of tracing out a subsystem, and the compatibility of multiple time axes in bipartite quantum interactions. Notably, we demonstrate that when a bipartite interaction is consistent with more distinct local temporal axes, there is a reduced allowance for information exchange between the two parties in order to prevent causality violations.