Designing a Universal Quantum Switch for Arbitrary Quantum Dynamics

TL;DR

This paper introduces the universal quantum switch (UQS), a novel superoperator capable of superposing arbitrary quantum dynamics, including non-CP-divisible ones, and demonstrates its advantages and properties through theoretical analysis and examples.

Contribution

The paper presents the UQS, a universal quantum switch that can superpose any set of quantum dynamics regardless of CP-divisibility, expanding the capabilities of quantum causal order manipulation.

Findings

UQS can superpose CP-divisible and non-CP-divisible dynamics.

The dynamics created by UQS can be CP-divisible or CP-indivisible.

Traditional quantum switches can alter the divisibility properties of quantum dynamics.

Abstract

A quantum switch is a superoperator that, in general, creates a superposition of various causal orders of two or more quantum dynamics that are all divisible in the complete positivity (CP) sense. We introduce a process that we term as the universal quantum switch (UQS), which unlike conventional quantum switches, allows for the construction of a quantum switch that can superpose different causal orders of any set of quantum dynamics, regardless of their CP-divisibility. Our approach also enables the construction of a quantum switch while considering a single environment connected with the system, in contrast to the traditional one. Moreover, we show the UQS provides more advantages in performance for a certain state discrimination task compared to traditional quantum switches. The next question that we address is the following: What is the CP-divisibility characteristic of a dynamics built by acting a quantum switch on CP-divisible or -indivisible dynamics? In this regard, an example is presented where the dynamics created by the action of the UQS on two CP-indivisible dynamics is CP-indivisible. Additionally, we prove a necessary and sufficient condition for the channel created by acting the traditional quantum switch on two CP-divisible dynamics to be CP-divisible. Furthermore, we present some examples of CP-divisible dynamics on which, when the usual quantum switch is operated, the resulting dynamics not only becomes CP-indivisible but also turns into P-indivisible. Our findings demonstrate that quantum switches can build CP-divisible, CP-indivisible, and even P-indivisible dynamics from CP-divisible dynamics, underscoring the versatility of this technique.