Related papers: Quantum Discrepancy: A Non-Commutative Version of …
Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of non-orthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination (QPD) of…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…
Modal interpretations constitute a particular approach to associating dynamical variables with physical systems in quantum mechanics. Given the `quantum logical' constraints that are typically adopted by such interpretations, only certain…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set…
We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
An apparatus model with discrete momentum space suitable for the exact solution of the problem is considered. The special Hamiltonian of its interaction with the object system under consideration is chosen. In this simple case it is easy to…
Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…