Related papers: Alignment of reference frames and an operational i…
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…
We show that sharing a quantum reference frame requires sharing measurement operators that identify the reference frame in addition to operators that measure its state. Observers restricted to finite resources cannot, in general,…
The emerging problem of joint community detection and group synchronization, with applications in signal processing and machine learning, has been extensively studied in recent years. Previous research has predominantly focused on a…
Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for…
Quantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to…
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time -reversal superselection so that two parties lacking knowledge about the other's direction of time can still…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
This work is a simple extension of \cite{NNjpa}. We apply the concepts of information geometry to study the mean-field approximation for a general class of quantum statistical models namely the higher-order quantum Boltzmann machines…
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
We present a theory of "quantum references", similar to lenses in classical functional programming, that allow to point to a subsystem of a larger quantum system, and to mutate/measure that part. Mutable classical variables, quantum…
The observable spacetime can be viewed as worldline coincidences (events) between a particle system and the observers of an extended (material) reference frame (ERF). Particle positions are then operationally well defined with respect to…