Certifying the dimensionality of any quantum channel with minimal assumptions

TL;DR

This paper introduces a universal, assumption-free method to certify whether quantum channels can preserve high-dimensional entanglement, crucial for quantum information tasks, without relying on idealized conditions.

Contribution

The authors develop a faithful certification method applicable to any quantum channel, avoiding common assumptions and extendable to other non-resource-breaking channels.

Findings

Method can certify entanglement dimensionality preservation

Applicable to any quantum channel without assumptions

Potential for experimental implementation

Abstract

High-dimensional entanglement offers significant advantages over low-dimensional ones in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as reliable preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-NPT-breaking channels. Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.