Coherence, asymmetry, and quantum macroscopicity

Abstract

We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a weighted sum of asymmetry in each mode can be applied as a measure of macroscopic coherence. To exclude the effects of microscopic superpositions, we suggest a method to introduce a cutoff to the weighted sum that will specify the macroscopic portion of the coherence. This cutoff may be interpreted as the fuzziness for a given measurement outcome. Based on the suggested measures, we investigate the quantum macroscopicity for particular concrete examples in N -partite spin systems.

Family of coherence measures and duality between quantum coherence and path distinguishability

“…After the completion of this work we were informed by Hyukjoon Kwon that 1/2-affinity of coherence has been computed and proven to be a coherence measure independently in Refs. [64,65] by different methods, yielding the same result. The other part can be proved as in Ref.…”

Existence of maximally correlated states

“…A measure satisfying this requirement is called entanglement monotone. Similar monotones have been defined for other quantum resources, such as nonuniformity, coherence, or asymmetry [9][10][11][12][13][14][15][16].…”

“…Note that here the codomains of the local operators K q,s and K q ′ ,s ′ can be different from one another provided q ′ = q. A very commun requirement for measures of entanglement or of any quantum resource [1,8,[10][11][12][13][14][15][16] reads here as follows. Condition 2.…”

“…This means that the average of the postmeasurement amounts of entanglement, each weighted with the corresponding measurement probability, is not larger than the premeasurement amount of entanglement. Other quantum resource monotones are nonincreasing on average under appropri-ate measurements [10][11][12][13][14][15][16].…”

Quantum asymmetry and noisy multi-mode interferometry

“…This is actually a subcase of the more general resource theory of quantum asymmetry [4,5], where the resource is the degree to which a quantum state breaks a certain symmetry, defined in terms of a Lie group. Quantum asymmetry has been recognized as the relevant physical resource in a variety of operational settings: reference frame alignment [6][7][8], quantum thermodynamic tasks [9][10][11], quantum speed limits [12,13], assessing macroscopic quantumness [14][15][16], and, most importantly for this work, quantum metrology [5,[17][18][19]. In this framework, the coherence of a quantum state with respect to the eigenspaces of an observable G corresponds to the asymmetry with respect to the one-parameter group of translations e iθG ; in the following, the term quantum asymmetry will be used to refer to this specific notion.…”