Related papers: On quantum tomography on locally compact groups
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are…
In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We develop the theory completely within the von Neumann algebra framework. At various points, we also do…
With steady progress in the development of quantum networks, the question on how to best provide end-to-end characterization of such networks (Quantum Network Tomography) is quickly becoming more pressing. Initial results demonstrated how…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…
The Haar measure on some locally compact quantum groups is constructed. The main example we treat is the az+b-group of Woronowicz. We also briefly consider some other examples (like the ax+b-group). We get the first examples of a locally…
We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the…
This manuscript is devoted to the study of the concept of a generating subset (a.k.a. Hopf image of a morphism) in the setting of locally compact quantum groups. The aim of this paper is to provide an accurate description of the Hopf image…
Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
The main aim of this paper is to introduce some examples of non-compact locally compact quantum groups to a non-specialized audience. The major importance of these examples is their simplicity. Other examples as the quantum E(2) group of…
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…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…