Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
By Iman Marvian, Robert W. Spekkens. 2013
134 citations recorded by the source corpus.
Finding the consequences of symmetry for open-system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology in the presence of noise. The symmetry of the dynamics may reflect a symmetry of the fundamental laws of nature or a symmetry of a low-energy effective theory, or it may describe a practical restriction such as the lack of a reference frame. In this paper, we apply some tools of harmonic analysis together with ideas from quantum information theory to this problem. The central idea is to study the decomposition of quantum operations\char22{}in particular, states, measurements, and channels\char22{}into different modes, which we call modes of asymmetry. Under symmetric processing, a given mode of the input is mapped to the corresponding mode of the output, implying that one can only generate a given output if the input contains all of the necessary modes. By defining monotones that quantify the asymmetry in a particular mode, we also derive quantitative constraints on the resources of asymmetry that are required to simulate a given asymmetric operation. We present applications of our results for deriving bounds on the probability of success in nondeterministic state transitions, such as quantum amplification, and a simplified formalism for studying the degradation of quantum reference frames.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/a8c9426aa63024f04a65a5596006d3420d834cb1
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- A mathematical theory of resources (2014, unknown): “…resources are quantum states that break a symmetry and quantum operations that fail to be covariant with respect to a symmetry [26, 38, 39, 40, 36, 37]; nonuniformity , where the resources are quantum states that deviate from the maximally mixed state and quantum operations that deviate from…”
- The role of quantum information in thermodynamics—a topical review (2015, background): “That direction of research can be related to the resource theory of quantum reference frames [89, 99–101].”
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “However, recent work has brought the concept of asymmetry to the fore, and shown it to be a valuable, consumable resource 23,31–35 .”
- Quantum resource theories (2018, background): “For example, when λn = n ∈ N, the state cos θ|0〉 + sin θ|1〉 can detect a phase shift of φ = π induced by the unitary e−iφT while the state cos θ|0〉+ sin θ|2〉 cannot (Marvian and Spekkens, 2014b, 2016).”
- Quantum processes which do not use coherence (2015, background): “The resource theory of quantum reference frames, or asymmetry [4, 37], has also been suggested as a framework for coherence [38].”
- Quantum coherence, time-translation symmetry and thermodynamics (2014, methodology): “The aim of this paper is to address this problem making use of recently developed tools from the resource theory of asymmetry [28,29].”