Entanglement-breaking channels are a quantum memory resource

TL;DR

This work challenges the common assumption that entanglement-breaking channels act solely as classical memory resources in temporal tasks. By analyzing a single quantum system undergoing repeated EB channels before measurements, the authors show that EB channels can generate nonclassical temporal correlations when memory is bounded, outperforming classical memories of the same dimension. They formalize a memory-cost framework using finite-state machines, derive classical bounds for sequence generation, and provide explicit quantum constructions (notably equiangular tight frames) that violate these bounds for certain sequence lengths. The findings reveal a nuanced interplay between quantum and classical resources in time and emphasize the need for careful memory accounting beyond the traditional EB-classical heuristic.

Abstract

Entanglement-breaking channels (equivalently, measure-and-prepare channels) are an important class of quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been employed in defining notions of "classical memory", under the assumption that such channels effectively act as a classical resource. We show that, in a single-system multi-time scenario, entanglement-breaking channels are still a quantum memory resource: a qudit going through an entanglement-breaking channel cannot be simulated by a classical system of same dimension. We provide explicit examples of memory-based output generation tasks where entanglement-breaking channels outperform classical memories of the same size. Our results imply that entanglement-breaking channels cannot be generally employed to characterize classical memory effects in temporal scenarios without additional assumptions.

Figures (3)

• Figure 1: Temporal correlations can be investigated by a classical or quantum system with $d$ distinguishable internal states, in the initial state $s_0$, which is repeatedly measured by the same instrument at multiple times. The measurement of state $s_t$ produces the outcome $a_{t+1}$ and changes the state to $s_{t+1}$.
• Figure 2: (a) The sequential measurement protocol considered in this work. An isolated quantum system in an initial state $\rho_0$ is repeatedly passed through an entanglement-breaking channel $\mathcal{E}$ before being measured by a quantum instrument $\mathcal{I}$, obtaining a sequence of outcomes $\boldsymbol{a} = a_1 a_2 \dots a_L$. (b) The entanglement-breaking channel $\mathcal{E}$ understood as a measure-and-prepare operation on a $d$-dimensional quantum system, with a $m$-dimensional intermediate classical space. (c) The $m \times m$ transition matrix of the effective classical model.
• Figure 3: Probabilities of one-tick sequences $\boldsymbol{a}^L_\text{ot}$ for classical one-way models (cf. Ref. budroni2021_tickingclocksvieira2022_temporal) and the quantum construction using ETFs, both using $d = L-1$. One-way models are conjectured to be optimal for all $L = d-1$, and are known to achieve the exact upper bounds $\Omega_C(\boldsymbol{a}^L_\text{ot},d)$ for $L = 3, 4$, and $5$. The bounds for $L = 4$ and $5$ are violated by this explicit quantum construction using ETFs, revealing nonclassical memory effects of EB channels.