Generalised tensors and traces

TL;DR

This paper generalizes tensors and trace operations to allow flexible system partitioning based on logical predicates, preserving key quantum properties through a new concept called consistency.

Contribution

It introduces a generalized framework for tensors and traces that maintains fundamental quantum relations under complex system partitioning, with the novel notion of consistency.

Findings

Key quantum properties are preserved under generalized partitions.

The framework introduces the concept of consistency for logical system partitioning.

Standard quantum relations remain valid in the generalized setting.

Abstract

Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through, although a new notion, consistency, becomes instrumental.