Related papers: Minimal sufficient statistical experiments on von …
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVM's into POVM's, generally irreversibly, thus loosing some of the…
The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., to a von Neumann measurement. Recently, generalized quantum coherence with respect to general positive operator-valued measurements (POVMs) has been…
In this work we study the phenomenon of self-testing from the first principles, aiming to place this versatile concept on a rigorous mathematical footing. Self-testing allows a classical verifier to infer a quantum mechanical description of…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
A measurement on a section K of the set of states of a finite dimensional C*-algebra is defined as an affine map from K to a probability simplex. Special cases of such sections are used in description of quantum networks, in particular…
This paper presents a simple yet efficient method for statistical inference of tensor linear forms using incomplete and noisy observations. Under the Tucker low-rank tensor model and the missing-at-random assumption, we utilize an…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete…
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…
The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von…
We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a…
We give a new definition of self-testing for correlations in terms of states on $C^*$-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed,…
We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
We consider a quantum probe $P$ undergoing pure dephasing due to its interaction with a quantum system $S$. The dynamics of $P$ is then described by a well-defined sub-algebra of operators of $S,$ i.e. the "accessible" algebra on $S$ from…
Every theory of information, including classical and quantum, can be studied in the framework of operational probabilistic theories--where the notion of test generalizes that of quantum instrument, namely a collection of quantum operations…
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that…