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Weight-based measure of quantum memory as a universal and operational benchmark

Jinghang Zhang, Yu Luo

TL;DR

The paper introduces a universal benchmarking approach for quantum memory by defining a weight-based memory measure, C_w, computed from the Choi state and constrained by EB (entanglement-breaking) channels. It provides a conic-program/SDP formulation, proves monotonicity under free super-operations, and establishes a general lower bound linked to channel robustness. An operational interpretation is given via nonlocal exclusion tasks, where the maximal payoff equals 1 minus the memory weight, highlighting concrete memory advantages over classical strategies. The authors compute C_w for several channel families (unitary, depolarising, maximal replacement, stochastic damping, and erasure channels), revealing a spectrum from perfect to vanishing memory and illustrating the benchmark's practical relevance for memory design and evaluation.

Abstract

Quantum memory plays a critical role in quantum communication, sensing, and computation. However, studies on quantum memory under a unified benchmarking framework remain scarce. In this paper, we propose a weight-based quantifier as a benchmarking method to evaluate the performance advantage of quantum memory in nonlocal exclusion tasks. We establish a general lower bound for the weight-based measure of quantum memory. Moreover, this measure provides fundamental theoretical bounds for transforming a general channel into an ideal quantum memory. Finally, we present explicit calculations of the weight-based quantifier for various channels, including unitary channels, depolarizing channels, maximal replacement channels, stochastic damping channels, and erasure channels.

Weight-based measure of quantum memory as a universal and operational benchmark

TL;DR

The paper introduces a universal benchmarking approach for quantum memory by defining a weight-based memory measure, C_w, computed from the Choi state and constrained by EB (entanglement-breaking) channels. It provides a conic-program/SDP formulation, proves monotonicity under free super-operations, and establishes a general lower bound linked to channel robustness. An operational interpretation is given via nonlocal exclusion tasks, where the maximal payoff equals 1 minus the memory weight, highlighting concrete memory advantages over classical strategies. The authors compute C_w for several channel families (unitary, depolarising, maximal replacement, stochastic damping, and erasure channels), revealing a spectrum from perfect to vanishing memory and illustrating the benchmark's practical relevance for memory design and evaluation.

Abstract

Quantum memory plays a critical role in quantum communication, sensing, and computation. However, studies on quantum memory under a unified benchmarking framework remain scarce. In this paper, we propose a weight-based quantifier as a benchmarking method to evaluate the performance advantage of quantum memory in nonlocal exclusion tasks. We establish a general lower bound for the weight-based measure of quantum memory. Moreover, this measure provides fundamental theoretical bounds for transforming a general channel into an ideal quantum memory. Finally, we present explicit calculations of the weight-based quantifier for various channels, including unitary channels, depolarizing channels, maximal replacement channels, stochastic damping channels, and erasure channels.

Paper Structure

This paper contains 18 sections, 8 theorems, 89 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Resource theories of quantum memory
  5. Main Results
  6. Weight-based measure of quantum memory
  7. The performance advantage of quantum memory in nonlocal exclusion task
  8. Fundamental limitations on the performance of the identity channel distillation protocol
  9. Examples of the weighted-based measure of quantum memory
  10. Unitary channels
  11. Depolarising channels
  12. Maximal replacement channels
  13. Stochastic damping channels
  14. Erasure channels
  15. Discussion and Conclusion
  16. ...and 3 more sections

Key Result

Proposition 1

The weight-based measure of quantum memory satisfies monotonicity, i.e., where $\Theta=\sum_{x}\Theta^x_{A\to B}$ is a superchannel and $p_x=\frac{1}{|B_0|}Tr[\mathcal{J}_{\Theta_x[\mathcal{N}]}]$.

Figures (3)

  • Figure 1: Achieving a superchannel and its effect on the input channel through pre-processing and post-processing of the channel.
  • Figure 2: Different quantum memory resource theories. (a) shows an EB memory, whose function is to eliminate all quantum entanglement, while (b) depicts an ideal memory that can losslessly preserve the original quantum state.
  • Figure 3: To display and compare the variation of the weight-based measure of different quantum channels with respect to the parameter $p$.

Theorems & Definitions (8)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6
  • Proposition 7
  • Proposition 8