General Theory of Coherence

Miguel Orszag

Nicky Joseph Hubertus Catharina Hacquier

This paper analyzes the Quantum Galileo Interferometer as an external weak-field constraint on coherence-modified gravitational models, using General Coherence Field Theory (GCFT) as a structured test case. It reconstructs the finite-pulse quantum-mechanical phase baseline, distinguishes experimentally constrained residual classes, defines the currently admitted GCFT matter–gravity interface, and identifies the missing terrestrial coherence-source model required for a numerical GCFT prediction. The work does not claim a detection of GCFT, quantum gravity, quantized gravity, or a universal numerical bound on the coherence field.

G. M. Bosyk, Marcelo Losada, César Massri +2 more

One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreover, using this notion and the majorization relation, we obtain a necessary condition for the conversion of general quantum states by means of incoherent operations. These results generalize the necessary conditions of conversions for pure states given in the literature, and show that the tools of the majorization lattice are useful also in the general case. Finally, we introduce a family of coherence quantifiers by considering concave and symmetric functions applied to the generalized coherence vector. We compare this proposal with the convex roof measure of coherence and others quantifiers given in the literature.

Miguel Orszag

Jianwei Xu

The standard quantum coherence theory is defined with respect to an orthonormal basis of a Hilbert space. Recently, Bischof, Kampermann and Bru% ß generalized the notion of coherence into the case of general measurements, and also, they established a rigorous resource theory of coherence with respect to general measurements. In this paper, we propose such a coherence measure with respect to general measurements via quantum Fisher information, and provide an application of this measure.