[Paper Review] Activating information backflow with the assistance of quantum SWITCH

Ananda G. Maity, Samyadeb Bhattacharya|arXiv (Cornell University)|Jun 9, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper demonstrates that quantum SWITCH can activate information backflow in dynamical maps that are non-Markovian yet do not exhibit backflow under standard conditions. By superposing the order of two such channels, the effective dynamics lose both CP- and P-divisibility, triggering previously hidden non-Markovianity, which cannot be activated through serial or parallel combinations of the same channels.

ABSTRACT

There are certain dynamics while being non-Markovian, do never exhibit information backflow. We show that if two such dynamical maps are considered in a scenario where the order of application of these two dynamical maps are not definite, the effective channel can manifest information backflow. In particular, we use quantum SWITCH to activate such a channel. In contrast, activation of those channels are not possible even if one uses many copies of such channels in series or in parallel action. We then investigate the dynamics behind the quantum SWITCH experiment and find out that after the action of quantum SWITCH both the CP (Complete Positive)- divisibility and P (Positive)- divisibility of the channel breaks down, along with the activation of information backflow. Our study elucidate the advantage of quantum SWITCH by investigating its dynamical behavior.

Motivation & Objective

• To investigate whether information backflow can be activated in non-Markovian channels that do not exhibit it under standard dynamics.
• To determine whether standard methods like serial or parallel concatenation of channels can activate hidden non-Markovianity.
• To explore the role of indefinite causal order via quantum SWITCH in enabling information backflow in otherwise non-backflow channels.
• To analyze the dynamical breakdown of CP and P divisibility in the switched channel as the root cause of activated non-Markovianity.

Proposed method

• The authors use the quantum SWITCH protocol to coherently superpose the order of two quantum channels that are individually non-Markovian but do not exhibit information backflow.
• They model the effective channel as a combination of two dynamical maps with time-dependent decay rates Γ₁, Γ₂, and Γ₃, where Γ₃ = −tanh(t).
• The analysis focuses on the divisibility properties of the effective channel, specifically checking for CP-divisibility and P-divisibility.
• They derive a condition for the onset of information backflow by analyzing the time derivative of the trace distance between two initial states.
• The characteristic time t* for the earliest backflow is calculated by solving A(t*) − B(t*) = 0, where A(t) and B(t) are time-evolving amplitude functions.
• Numerical and analytical solutions confirm that t* ≈ 0.67 when the initial state is |1⟩⟨1| and |2⟩⟨2|, matching simulation results.

Experimental results

Research questions

• RQ1 Can information backflow be activated in non-Markovian channels that do not show it under standard dynamical evolution?
• RQ2 Is the activation of information backflow possible through serial or parallel combinations of such channels?
• RQ3 What is the dynamical mechanism behind the activation of non-Markovianity via quantum SWITCH?
• RQ4 How do CP-divisibility and P-divisibility break down in the switched channel to enable backflow?
• RQ5 What role does the initial state play in determining the onset time of information backflow?

Key findings

• Information backflow is successfully activated in channels that are non-Markovian but do not exhibit backflow under standard dynamics, using quantum SWITCH.
• The activation is not achievable through any number of serial or parallel combinations of the same channels, highlighting the unique role of indefinite causal order.
• The effective switched channel breaks both CP-divisibility and P-divisibility, which is the fundamental mechanism enabling information backflow.
• The earliest time at which information backflow can be triggered is t* ≈ 0.67, derived from the condition A(t*) − B(t*) = 0 for the given initial state.
• The onset time t* depends on the initial state parameters, with the condition e^{t*}(A(t*) − B(t*))/A(t*) = ±χ(0) governing the solution.
• The analytical solution for t* matches the numerical results shown in Fig. 3, confirming the consistency of the model.