The quantum de Finetti representation for the Bayesian Quantum Tomography and the Quantum Discord

TL;DR

This paper reveals that the quantum de Finetti representation, while useful for exchangeable systems, assigns non-zero quantum discord to uncorrelated states, challenging its role as a universal prior in Bayesian quantum tomography due to the linearity of the Born rule.

Contribution

It identifies a fundamental limitation of the quantum de Finetti representation in Bayesian quantum tomography related to quantum discord and the linearity of quantum probability assignments.

Findings

Quantum de Finetti assigns non-zero discord to uncorrelated states.

The linearity of the Born rule causes mixing of knowledge and state representation.

This mixing limits the de Finetti's universality as a prior in Bayesian tomography.

Abstract

We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the Bayesian Quantum Tomography. This apparent paradox stems from linearity of the Born rule for the probability assignment in Quantum Mechanics, which results in mixing of one's knowledge about the quantum state and the representative of the state in one density matrix.