Limits on the Observable Dynamics of Mixed States

TL;DR

This paper establishes fundamental limits on observing the effects of certain quantum operations on mixed states, showing that for maximally mixed states, these operations are inherently unobservable due to purity-dependent bounds.

Contribution

It introduces a purity-dependent upper bound on the trace distance for unital operations, highlighting fundamental observability limitations on mixed states.

Findings

Maximally mixed states render certain operations unobservable.

Derived an upper bound on trace distance based on state purity.

Operations within the considered class are unobservable at maximal mixedness.

Abstract

It is shown that the observability of a large class of operations on mixed states is fundamentally limited. We consider trace preserving, unital operations. This class includes unitary and perfect premeasurement operations. An upper bound on the trace distance between an untransformed state and a state transformed by one of these operations is derived. The bound is dependent only on the purity of the state. In the case of maximal mixedness, the bound implies all operations of this class are unobservable.