The resource theory of quantum reference frames: manipulations and monotones

By Gilad Gour, Robert W. Spekkens. 2007

408 citations recorded by the source corpus.

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule (SSR) is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of SSRs, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focusing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically non-increasing under various classes of operations that are permitted by the SSR.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/03f5280bd24f44ab99f88b1893953083562f3458

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Citations in the corpus

Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “…certain aspects of quantum mechanics such as entanglement (Horodecki et al., 2009), athermality (Goold et al., 2016; Gour et al., 2015), asymmetry (Gour and Spekkens, 2008) and coherence (Baumgratz et al., 2014; Marvian and Spekkens, 2016; Yadin et al., 2016) in the framework of resource theories.”
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “functions that do not increase under symmetric evolution [32], can impose further, non-trivial constraints on the dynamics [22] (See methods for a brief discussion of the connections between the present approach and fluctuation theorems).”
The resource theory of informational nonequilibrium in thermodynamics (2013, background): “…(Horodecki et al., 2009), the restriction to symmetric quantum operations defines the resource theory of asymmetry (Bartlett et al., 2007; Gour and Spekkens, 2008; Marvian and Spekkens, 2011), and the restriction to stabilizer operations defines a theory of quantum computational…”
A mathematical theory of resources (2014, neutral): “…[30] pairs of bipartite LOCC operations Hilbert spaces n -partite entanglement n -tuples of n -partite LOCC operations Hilbert spaces asymmetry [26, 38] pairs of a Hilbert space G -covariant operations (relative to a symmetry group G ) & a unitary rep’n of G nonuniformity [27, 25] Hilbert…”
Irreversible entropy production: From classical to quantum (2020, background): “The resource theory of asymmetry (also called quantum reference frames) concerns arbitrary transformations under a certain group (Gour and Spekkens, 2008).”
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].”
Fundamental limitations for quantum and nanoscale thermodynamics (2011, background): “Recent examples of such theories include entanglement theory[20, 29], thermodynamics with no Hamiltonian[19], thermodynamics of erasure[30] and operations which respect a symmetry[31, 32].”
Entanglement theory and the second law of thermodynamics (2008, background): “The paradigm that we put forward could also potentially be helpful in the study of non-locality of quantum states, of super-selections rule”
Quantum resource theories (2018, background): “Originally, it was coined by Schumacher in 2003 (unpublished), and later in a 2008 paper on the resource theory of quantum reference frames (Gour and Spekkens, 2008).”
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].”