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We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
Recent studies have introduced the worst-case quantum divergence as a key measure in quantum information. Here we show that such divergences can be understood from the perspective of the resource theory of asymmetric distinguishability,…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
In this tutorial, we present the definition, interpretation and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…
I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large…
Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for…
Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
In this contribution, we aim to illustrate how quantum work statistics can be used as a tool in order to gain insight on the universal features of non-equilibrium many-body systems. Focusing on the two point measurement approach to work, we…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with…
This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being…
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
The general notion of distance dependent statistics in anyon-like systems is discussed. The two-body problem for such statistics is considered, the general formula for the second virial coefficient is derived and it is shown that in the…