Quantum Coherence and Distinguishability: A Resource-Theoretic Perspective on Wave-Particle Duality

2024-04-22

arXiv.org

AI Summary

This work investigates the complementarity between quantum coherence (wave-like behavior) and classical distinguishability (particle-like behavior) under incoherent operations, aiming to generalize beyond conventional interference settings and establish a universal quantum–classical resource duality principle. Method: Leveraging quantum resource theory, we integrate the framework of perfect discrimination of orthogonal pure states with information conservation analysis. Contribution/Results: We introduce and rigorously prove, for the first time, a tight upper bound on the sum of coherent bits (co-bits) and classical bits in any orthogonal ensemble. This bound quantitatively captures the fundamental trade-off between extracting coherence and classical distinguishability during information processing, revealing wave–particle duality as an intrinsic duality between quantum coherence resources and classical distinguishability resources. Our results elevate Bohr’s complementarity principle to the level of quantum resource theory, providing a new paradigm for quantum measurement, information encoding, and foundational interpretation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Wave-particle duality, the cornerstone of quantum mechanics, illustrates essential trade-offs between two complementary aspects of quantum systems. Captured by Bohr's complementarity principle, the wave-particle duality relation indicates that perfect path discrimination in a multipath interferometer obliterates interference patterns and vice versa. In this work, from the perspective of coherence resource manipulation, we uncover a novel duality relation between quantum coherence and distinguishability in ensembles of mutually orthogonal pure states. We demonstrate the sum of `co-bits', coherence preserved after discrimination, and classical bits, distinguishability extracted through perfect discrimination is bounded. One cannot simultaneously extract all classical information and preserve coherence. Such duality relation exposes an inherent trade-off between quantum coherence and classical distinguishability resources. Our findings offer a fresh perspective and advance our understanding of the intrinsic complementary relationship between quantum and classical resources.

Problem

• Explores duality between quantum coherence and classical distinguishability
• Proves trade-off in preserving coherence versus extracting distinguishability
• Extends wave-particle duality via quantum resource theories

Innovation

• Treat coherence and distinguishability as complementary resources
• Prove coherence-distinguishability duality relation in ensembles
• Explore quantum state discrimination under incoherent operations