Extendible quantum measurements and limitations on classical communication

2024-12-24

AI Summary

This work investigates fundamental limitations imposed by quantum measurements on classical information transmission, particularly under the no-cloning constraint, with a focus on how *k*-extendibility of measurements affects the classical capacity of quantum channels. We introduce the first formal definition of *k*-extendible measurements and establish a hierarchical semidefinite programming (SDP) characterization framework. This framework rigorously quantifies the approximation capability and convergence behavior of measurements implementable via local operations and classical communication (LOCC), proving that the hierarchy converges asymptotically to the set of one-way LOCC measurements. Theoretically, we derive a single-shot upper bound on classical capacity that strictly improves upon the Matthews–Wehner bound. Algorithmically, we provide an efficiently computable upper bound on the *n*-shot capacity. Our results establish a novel resource-theoretic framework for quantum measurements and deliver tight, computationally tractable tools for analyzing communication capacities under measurement constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications in providing limitations on quantum error correction and entanglement distillation. Here we generalize the framework of unextendibility to quantum measurements and define $k$-extendible measurements for every integer $kge 2$. Our definition provides a hierarchy of semidefinite constraints that specify a set of measurements containing every measurement that can be realized by local operations and one-way classical communication. Furthermore, the set of $k$-extendible measurements converges to the set of measurements that can be realized by local operations and one-way classical communication as $k o infty$. To illustrate the utility of $k$-extendible measurements, we establish a semidefinite programming upper bound on the one-shot classical capacity of a channel, which outperforms the best known efficiently computable bound from [Matthews and Wehner, IEEE Trans. Inf. Theory 60, pp. 7317-7329 (2014)] and also leads to efficiently computable upper bounds on the $n$-shot classical capacity of a channel.

Problem

• Quantum Measurement
• Information Transmission
• No-Cloning Theorem

Innovation

• k-extendibility
• quantum measurement
• information transmission efficiency