The Operational Choi-Jamiolkowski Isomorphism

TL;DR

This paper presents an operational perspective on the Choi-Jamiołkowski isomorphism, showing that quantum features typically attributed to states can be derived from correlation constraints, challenging the notion of states as fundamental objects.

Contribution

It introduces an operational formulation of the Choi-Jamiołkowski isomorphism and demonstrates how quantum properties can emerge from correlation constraints without assuming states as fundamental.

Findings

Quantum properties derive from correlation constraints.

The isomorphism links multipartite and temporal correlations.

States are not necessary as fundamental objects.

Abstract

In this article, I use an operational formulation of the Choi-Jamio\l{}kowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi-Jamio\l{}kowski isomorphism and show that in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.