相关论文: Projective invariant measures and approximation of…

The present work develops a framework to derive piecewise polynomial measures arising from invariant measures on adjoint orbits in the context of compact and semisimple Lie groups. These measures are computed from orbital integrals via…

We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…

The effects of different forms of weak measurements on the nature of the measurement induced phase transition are theoretically studied in hybrid random quantum circuits of qubits. We use a combination of entanglement measures, ancilla…

Symmetries are crucial for tailoring parametrized quantum circuits to applications, due to their capability to capture the essence of physical systems. In this work, we shift the focus away from incorporating symmetries in the circuit…

Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak…

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…

In this paper, we establish an abstract framework for the approximation of the invariant probability measure for a Markov semigroup. Following Pag{\`e}s and Panloup [40] we use an Euler scheme with decreasing step (unadjusted Langevin…

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…

The aim of the article is to show how a coordinate transformation can be applied to the path-integral formalism. For this purpose the unitary definition of the quantum measure, which guarantees the conservation of total probability, is…

For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…

This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential…

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability…

Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only…

We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…

The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…

We represent quantum observables as POVMs (normalized positive operator valued measures) and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group $G$.…

We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski…