Related papers: A simple operational interpretation of the fidelit…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
We suggest new types and interpretation of complex and hypercomplex numbers for which the commutative, associative, and distributive laws and the norm axioms are trivially satisfied.
We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.
We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability modality and the interpretability modality can come with a label. This label indicates that in the arithmetical interpretation the axiom set of…
We discuss a new approach to functional interpretations based on uniform quantification and relativization. The uniform quantification in the background permits a more penetrating analysis of principles related to collection and…
Ordinal analysis induces a partition of $\Sigma^1_1$-definable and $\Pi^1_1$-sound theories whereby two theories are equivalent if they have the same proof-theoretic ordinal. We show that no equivalence relation $\equiv$ is finer than the…
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…
We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.
We reduce the Openness Conjecture of Demailly and Koll\'ar on the singularities of plurisubharmonic functions to a purely algebraic statement.
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Computation of Uhlmann fidelity between many-body mixed states generally involves full diagonalization of exponentially large matrices. In this work, we introduce a polynomial-time algorithm to compute certified lower and upper bounds for…
The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on K\"ahler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here…
In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system…