On the information completeness of quantum tomograms

TL;DR

This paper investigates the conditions under which quantum tomograms, especially symplectic ones, can fully determine quantum states, introducing a measure of information completeness and exploring cases with incomplete data.

Contribution

It proposes a measure of information completeness for quantum tomograms and demonstrates scenarios where incomplete tomograms suffice for state reconstruction with prior knowledge.

Findings

Incomplete tomograms can still enable state reconstruction with prior info.

A new measure of information completeness for quantum tomograms is introduced.

Specific conditions for symplectic tomograms to be informationally complete are identified.

Abstract

We address the problem of information completeness of quantum measuremets in connection to quantum state tomography and with particular concern to quantum symplectic tomography. We put forward some non-trivial situations where informationally incomplete set of tomograms allows as well the state reconstruction provided to have some a priori information on the state or its dynamics. We then introduce a measure of information completeness and apply it to symplectic quantum tomograms.