Measuring the quality of a quantum reference frame: The relative entropy of frameness

By Gilad Gour, Iman Marvian, Robert W. Spekkens. 2009

195 citations recorded by the source corpus.

In the absence of a reference frame for transformations associated with group G, any quantum state that is noninvariant under the action of G may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest G-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the G-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to boundingmore » the relative entropy of entanglement.« less

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/408eea3c8d7db41a4689c59d1cd5e1113d000e8d

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Citations in the corpus

The resource theory of stabilizer quantum computation (2013, methodology): “This was pointed out in [20], and the theorem we state here is essentially the application of their Theorem 4 to magic theory.”
A mathematical theory of resources (2014, unknown): “[24], was that the result of Ref.”
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “For α→ 1, we have A1(ρ) ≡ A(ρ) which is the asymmetry measure introduced in [33, 36, 37].”