Related papers: A generalization of Schur-Weyl duality with applic…
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and therefore,…
We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this…
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…
It is well-known that the commutant algebra of the $U_q(\mathfrak{sl}_2)$-action on the $n$-fold tensor product of its fundamental module is isomorphic to the Temperley-Lieb algebra TL$_n(\nu)$ with fugacity parameter $\nu = -q - q^{-1}$…
Quantum systems can display particle- or wave-like properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement…
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This…
Quantum state estimation for continuously monitored dynamical systems involves assigning a quantum state to an individual system at some time, conditioned on the results of continuous observations. The quality of the estimation depends on…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without…
Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data-processing of the measurement outcomes. In particular, an informationally complete measurement…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation. I assume that (i) the quantum state is a…