Related papers: Bounds on positive operator-valued measure based c…
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These…
We report an optical detector with tunable positive operator-valued measures (POVMs). The device is based on a combination of weak-field homodyne techniques and photon-number-resolving detection. The resulting POVMs can be continuously…
Quantum state tomography seeks to reconstruct an unknown state from measurement statistics. A finite measurement (POVM) is \emph{pure-state informationally complete} (PSI-Complete) if the outcome probabilities determine any pure state up to…
In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case.…
Recently foundational issues of applicability of the formalism of quantum mechanics (QM) to cognitive psychology, decision making, and psychophysics attracted a lot of interest. In particular, in \cite{DKBB} the possibility to use of the…
We introduce a resource monotone, the completeness stability, to quantify the quality of quantum measurements within a resource-theoretic framework. By viewing a quantum measurement as a frame, the minimum eigenvalue of a frame operator…
In the resource theory of coherence, the quantification of quantum-state coherence is an important task. In this regard, the key ingredients are the various coherence monotones (or measures). There are few coherence-monotone classes that…
The concepts of `conditional entropy' and `information' retain their validity for quantum systems, but their properties differ somewhat from those of their classical counterparts; specifically, some equalities and inequalities of classical…
Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine…
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert…
Many symmetry protected or symmetry enriched phases of quantum matter have the property that every ground state in a given such phase endows measurement based quantum computation with the same computational power. Such phases are called…
Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing,…
Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. In this work we consider a figure of merit encoding the information on how the coherence generated on average by a…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1)…
The quantification of quantum coherence has attracted a growing attention, and based on various physical contexts, several coherence measures have been put forward. An interesting question is whether these coherence measures give the same…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…