Trace decreasing quantum dynamical maps: Divisibility and entanglement dynamics

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.

Multiletter codes to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses

“…The study in Sections II, III, and IV was supported by the Russian Science Foundation under Project No. 19…”

“…The superadditivity phenomenon is predicted for qubit depolarizing channels if n ≥ 3 [9,10], so-called dephrasure qubit channels if n ≥ 2 [11] (for which superadditivity was also analyzed experimentally [12]), a concatenation of an erasure qubit channel with an amplitude damping qubit channel [13], some qutrit channels and their higher-dimensional generalizations [14], and a collection of specific channels if n ≥ n 0 , where n 0 ≥ 2 can be arbitrary [15]. In this paper, we focus on quantum communication lines with polarization dependent losses [16][17][18][19][20], which also exhibit the coherent information superadditivity for some values of attenuation factors [21].…”

Entanglement robustness in trace decreasing quantum dynamics caused by depolarization and polarization dependent losses

“…Note that the map (0) → (t) in nonlinear, so focusing solely on the dynamics of (t) may lead to a misidentification of non-Markovianity of Λ(t) [21].…”