Trace decreasing quantum dynamical maps: Divisibility and entanglement dynamics

TL;DR

This paper investigates the properties of trace decreasing quantum maps, revealing that common experimental assumptions can lead to incorrect conclusions about their divisibility and entanglement dynamics, and proposes methods to correctly analyze these phenomena.

Contribution

It introduces proper indicators for information backflow in trace decreasing quantum dynamics and reviews the generalized erasure dynamics concept with experimental relevance.

Findings

Trace decreasing dynamics can appear indivisible despite complete positivity.

Incorrect conclusions about divisibility can arise from analyzing conditional states.

Proper indicators are necessary for accurate assessment of quantum information flow.

Abstract

Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that this approach leads to incorrect conclusions about the dynamics divisibility, namely, one can observe an increase in the trace distance or the system-ancilla entanglement although the trace decreasing dynamics is completely positive divisible. We propose solutions to that problem and introduce proper indicators of the information backflow and the indivisibility. We also review a recently introduced concept of the generalized erasure dynamics that includes more experimental data in the dynamics description. The ideas are illustrated by explicit physical examples of polarization dependent losses.