Related papers: Proper Versus Improper Mixtures: Towards a Quatern…
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…
It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure (mixed) one represented by a density matrix. I…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow…
In this work we investigate the relation between quantum measurements and decoherence, in order to formally express the necessity of the latter for obtaining an informative output from the former. To this aim, referring to the Von Neumann…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
A common misconception is that decoherence gives the eigenstates that we observe to be fairly definite about a subsystem (e.g., approximate eigenstates of position) as the elements of the Schmidt basis in which the density matrix of the…
Protective measurement, which was proposed as a method of observing the wavefunction of a single system, is extended to the observation of the density matrix of a single system. d'Espagnat's definition of `proper mixture' is shown to be…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…
Different ensembles of quantum states can have the same average nonpure state. Distinguishing between such constructions, via different mixing procedures of the same nonpure quantum state, is known to entail signaling. In parallel,…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the…
This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The…
Uncertainties in the frequency parameters of a frequency comb laser, causes it to represent a mixed quantum state. The formulation of such a quantum state is compounded by the fact that it contains both particle-number degrees of freedom…