Related papers: A simple operational interpretation of the fidelit…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
Agents receive private signals about an unknown state. The resulting joint belief distributions are complex and lack a simple characterization. Our key insight is that, when conditioned on the state, the structure of belief distributions…
We present an efficient experimental estimation of the multipartite entanglement of mixed quantum states in terms of simple parity measurements.
The fidelity, defined as overlap of eigenstates of two slightly different Hamiltonians, is proposed as an efficient detector of avoided c rossings in the energy spectrum. This new application of fidelity is motivated for model systems, and…
We derive analytical formula for the optimal trade-off between the mean estimation fidelity and the mean fidelity of the qubit state after a partial measurement on N identically prepared qubits. We also conjecture analytical expression for…
This text can be considered as a non-technical and arithmetically motivated introduction to the definition of the limiting mixed Hodge structure. We state several assertions in terms natural to the classical theory of ordinary differential…
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…
We present probability-fidelity tradeoffs for a varying quantum operation with fixed input-output states and for a varying inversion of a fixed quantum operation.
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
The conformal invariance of Brownian motion is used to give a short proof of the Open Mapping Theorem for analytic functions.
In this work, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or $Z_{2}$ extension of the chiral Ising CFT) gives a…
We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in…
We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…