Related papers: On constructing informationally complete covariant…
In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…
We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and…
We present a systematic analysis on coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator.…
We study strongly measurable random bounded operators on separable Hilbert spaces and analyze two simple iterations driven by independent random positive contractions. The first, a Kaczmarz-like iteration, converges in mean square and…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
We prove the existence and uniqueness of a *projectively equivariant symbol map*, which is an isomorphism between the space of bidifferential operators acting on tensor densities over $R^n$ and that of their symbols, when both are…
Let I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H. Let ${p_i}_1 ^w$ $(1\leq w \leq \infty)$ be a family of mutually orthogonal projections on H. The pinching operator associated with the…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…
We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator…
Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which…
To optimize the entanglement detection, we formulate the metrologically operational entanglement condition in quantum Fisher information by maximizing the QFI on the measurement orbit. Specifically, we consider two classes of typical local…
The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces…
Uncertainty in the estimation of the causal effect in observational studies is often due to unmeasured confounding, i.e., the presence of unobserved covariates linking treatments and outcomes. Instrumental Variables (IV) are commonly used…
We study an extremal projection principle for families of operators ordered by domination, induced by fixed bounded linear mappings acting on a source with an additive baseline. Stability is defined through domination of second--order…
In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for…
Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are…
One of the most studied algebraic structures with one operation is the Abelian group, which is defined as a structure whose operation satisfies the associative and commutative properties, has identical element and every element has an…