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A new class of state transformations that are quantum mechanically prohibited is introduced. These can be seen as the generalization of the universal-NOT transformation which, for all pure inputs state of a given Hilbert space produces pure…
We compute the leading order corrections to the expected value of the squared field amplitude of a massless real scalar quantum field due to curvature in a localized region of spacetime. We use Riemann normal coordinates to define localized…
Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum…
We prove a general reduction theorem for stabilizer absolutely maximally entangled states in composite local dimension. If a stabilizer $\mathrm{AME}(n,D)$ state exists and $D=\prod_{i=1}^m q_i$ is the prime-power factorization of $D$, then…
The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…
The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The…
This is a revised version of the doctoral dissertation of the same title, written under the supervision of Professor Krzysztof Stempak in 2019. For general (possibly nondoubling) metric measure spaces various properties of the associated…
For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation [x_i,p_j]=i…
The main content of this treatise is a new concept in nonperturbative non-Lagrangian QFT which explains and extends the ad hoc constructions in low-dimensional models and incorporates them together with the higher dimensional theories into…
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 investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. We establish uncertainty principles for the characteristic function and the Wigner function of states,…
Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard…