Fundamental trade-off relation in probabilistic entanglement generation

TL;DR

This paper establishes a fundamental trade-off relation between success probability and entanglement in probabilistic quantum processes, revealing a quasi-deterministic mode of operation and demonstrating its realization via quantum switch, advancing entanglement control.

Contribution

It introduces a universal trade-off relation for entanglement generation, predicts a quasi-deterministic mode, and shows how to realize this using indefinite causal order in quantum switches.

Findings

Derived a universal trade-off bound $P_{\text{succ}}(1+\mathcal{C})\le1$.

Discovered a quasi-deterministic entanglement generation mode.

Validated the principles with concrete protocols and quantum switch implementations.

Abstract

We investigate the generation of entanglement between two non-interacting systems by synthesizing a new quantum process from the superposition of distinct processes characterized by local-only operations. Our analysis leads to the derivation of a universal trade-off relation, $P_{\text{succ}}(1+\mathcal{C})\le1$, that fundamentally bounds the success probability ($P_{\text{succ}}$) and the generated entanglement (concurrence $\mathcal{C}$). The derivation of this trade-off relation is inspired by indefinite causal order, but applies for a broader class of quantum processes. Next, we show that the mathematical structure of this bound predicts the existence of a "quasi-deterministic" mode of operation, a surprising phenomenon which we then confirm with concrete entanglement generation protocols, where a maximally entangled state is guaranteed to be produced. In this mode of operation, both outcomes of the post-selection measurement on the auxiliary control system result in a maximally entangled state of the target system. Furthermore, we demonstrate how this general principle can be realized using a quantum switch, which leverages an indefinite causal order as a physical resource, and explore the rich variety of dynamical behaviors governed by the universal trade-off. Our results establish a general principle for entanglement generation with superposition of quantum processes and introduce a novel way of controlling entanglement generation.