Related papers: The signaling dimension in generalized probabilist…
A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
We consider approximation of diameter of a set $S$ of $n$ points in dimension $m$. E$\tilde{g}$ecio$\tilde{g}$lu and Kalantari \cite{kal} have shown that given any $p \in S$, by computing its farthest in $S$, say $q$, and in turn the…
Establishing the correspondence of two dimensional paraxial and three dimensional non-paraxial optical beams with the qubit and qutrit systems respectively, we derive a complementary relation between Hilbert-Schmidt coherence, generalized…
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional…
We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood,…
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from…
The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement…
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are {\it particles}, elementary or composite. It follows that each elementary process, hence…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…