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arXiv:2307.08462 · Photonics Research

Experimental verification of a coherence factorization law for quantum states

Yi Zheng, Chengjie Zhang, Zhenghao Liu, Jian-Wei Shao, Jin‐Shi Xu, Chuan‐Feng Li, Guang‐Can Guo

Published Jul 19, 2022• 1 citation
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Abstract

As a quantum resource, quantum coherence plays an important role in modern physics. Many coherence measures and their relations with entanglement have been proposed, and the dynamics of entanglement has been experimentally studied. However, the knowledge of general results for coherence dynamics in open systems is limited. Here we propose a coherence factorization law that describes the evolution of coherence passing through any noisy channels characterized by genuinely incoherent operations. We use photons to implement the quantum operations and experimentally verify the law for qubits and qutrits. Our work is a step toward understanding of the evolution of coherence when the system interacts with the environment, and will boost the study of more general laws of coherence.

DOI
10.1364/prj.463829

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Abstract When a quantum system is sent through a noisy channel, it is usually disturbed. At the same time, the system undergoes decoherence and tends to lose some delicate quantum features. For a particular basis, the coherence of the state changes. Otherwise, if the system is not disturbed, its state might retain all of coherence. As quantum noisy channels lead to both disturbance and decoherence, it is natural to ask about the relation between disturbance and decoherence. Recently, a trade-off relation for coherence and disturbance has been presented by Sharma and Pati (2018 Phys. Rev. A 97 062308). In this paper, with entangled photon pairs and linear optics, we experimentally verify this trade-off relation for a single-qubit system undergoing various noisy channels. Our experimental results agree with the theoretical predictions and provide a quantitative understanding of the relation between quantum channels and resources.
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite entanglement that can be generated via incoherent operations applied to the system and an incoherent ancilla. The resulting measures are proven to be valid coherence monotones satisfying all the requirements dictated by the resource theory of quantum coherence. We demonstrate the usefulness of our approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Our work provides a clear quantitative and operational connection between coherence and entanglement, two landmark manifestations of quantum theory and both key enablers for quantum technologies.
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Quantum noise is ubiquitous to quantum systems as they incessantly interact with their surroundings and results in degrading useful resources such as coherence for single quantum systems and quantum correlations for multipartite systems. Given the importance of these resources in various quantum information processing protocols, it is of the utmost importance to characterize how deteriorating a particular noise scenario (quantum channel) is in reference to a certain resource. Here we develop a theory of coherence-breaking channels for single quantum systems. Any quantum channel on a single quantum system will be called a coherence-breaking channel if it is an incoherent channel and maps any state to an incoherent state. We explicitly and exhaustively characterize these coherence-breaking channels. Moreover, we define the coherence-breaking indices for incoherent quantum channels and present various examples to elucidate this concept. We further introduce the concept of coherence sudden death under noisy evolutions and make an explicit connection of the phenomenon of coherence sudden death with the coherence-breaking channels and the coherence-breaking indices together with various suggestive examples. Furthermore, for higher-dimensional Hilbert spaces, we establish the typicality of the dynamics of coherence under any incoherent quantum channel exploiting the concentration of measure phenomenon.