Related papers: Product Bases in Quantum Information Theory
The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the…
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…
In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The complete axiomatic…
We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
Two systems whose correlations cannot be classically accounted for display the simplest instance of quantum entanglement. Although this two-party association has caused a revolution in the foundations and uses of quantum mechanics, genuine…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
Let $X$ be the product of a surface satisfying $b_2=\rho$ and of a curve over a finite field. We study a strong form of the integral Tate conjecture for $1$-cycles on $X$. We generalize and give unconditional proofs of several results of…
We argue in a quantitative way that the unitarity principle of quantum field theory together with the quantum information bound on correlation functions are in tension with a space which is made out of disconnected patches at microscopic…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…
Quantum logical axiomatic systems for quantum theory usually include a postulate that a lattice under consideration is orthomodular. We propose a derivation of orthomodularity from an information-theoretic axiom. This provides conceptual…
Quantum measurements based on mutually unbiased bases (MUB) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUB, but little is known about their operational…
Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
We introduce a new family of indecomposable positive linear maps based on entangled quantum states. Central to our construction is the notion of an unextendible product basis. The construction lets us create indecomposable positive linear…
The purpose of this study is to explore whether the relationship between bias and nudges can be mathematically expressed in terms of quantum information theory, particularly by means of individually customized nudges. Based on the value…
All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive…