Quantum Coherence as a Resource (1609.02439v3)

Abstract: The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted a considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has only been initiated recently. In this Colloquium we discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

• The paper introduces a framework that defines and quantifies coherence similarly to quantum entanglement.
• It employs methodologies like distillable coherence and coherence cost to measure coherence in quantum processes.
• It explores practical applications of coherence in technologies such as quantum algorithms, metrology, and thermal machines.

Overview of "Colloquium: Quantum Coherence as a Resource"

The paper "Colloquium: Quantum Coherence as a Resource" authored by Alexander Streltsov, Gerardo Adesso, and Martin B. Plenio provides a comprehensive review of the role and quantification of quantum coherence as an essential resource in quantum mechanics. This document encapsulates the significant strides made in understanding coherence, its applications across various domains of physics, and its fundamental differentiation from classical physics. The paper further contributes by framing coherence within a resource-theoretic perspective, akin to more established concepts such as quantum entanglement.

Key Topics and Contributions:

1. Coherence and Quantum Mechanics:
   • Quantum coherence is central to the departure from classical physics. It underlines phenomena such as quantum interference and multipartite entanglement.
   • The paper emphasizes the historical significance of coherence in optical fields and its role in the development of technologies like lasers (termed as Quantum Technologies 1.0).
2. Resource Theory of Quantum Coherence:
   • Analogous to the resource theory of entanglement, the paper proposes a structured approach to defining, quantifying, and leveraging quantum coherence as a resource within physical and computational constraints.
   • Various sets of "incoherent operations" are introduced, addressing transformations which preserve or manipulate coherence using resources. These provide a mechanism to understand the functional power of coherence.
3. Quantification of Coherence:
   • Axiomatic frameworks for coherence measures are discussed, extending beyond simple quantification to more nuanced interpretations like "distillable coherence" and "coherence cost."
   • The relationship between coherence and entanglement is further explored, showing how entanglement quantifiers can be adapted to measure coherence.
4. Operational Interpretations:
   • Coherence is highlighted as a resource in several quantum processes like quantum algorithms, metrology, and communication protocols.
   • The coherence in open systems, coherence within biological systems, and the interplay between coherence and asymmetry are thoroughly analyzed.
5. Applications and Implications:
   • In thermodynamics, quantum coherence is discussed as a possible resource for tasks such as work extraction and the functioning of quantum thermal machines.
   • The paper showcases coherence's role in quantum speed limits, quantum channel discrimination, and in biological contexts like photosynthesis and magnetoreception.
6. Challenges and Future Directions:
   • A core challenge identified is defining universally agreed-upon measures and operations that preserve coherence as a distinct resource.
   • There is considerable interest in developing robust methods to experimentally access and manipulate quantum coherence to inform future technologies and understand its broad applications across science.

Implications and Future Prospects:

The paper delineates that while significant foundational work has been done, quantum coherence as a resource holds vast unexplored potential, especially in emerging quantum technologies (Quantum Technologies 2.0). The theoretical development provided offers a toolkit for future explorations into coherence-driven phenomena across physics, addressing practical and theoretical challenges in global quantum research structures. The implications range from enhancing quantum computational models to optimizing coherence in practical quantum systems, suggesting a future ripe with innovations driven by an enriched understanding of coherence.