Related papers: A transference method in quantum probability
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
If $A$ is in the $p$-Schatten class on $\mathbb{R}^n$, $1\leq p \leq \frac{4n}{2n-1}$, then the quantum translates of $A$ are linearly independent. Moreover, there exists a non-zero operator in the $p$-Schatten class on $\mathbb{R}^n$,…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
The quantum theory involving noncommutative tensionless p-branes is studied following path integral methods. Our procedure allow a simple treatment for generally covariant noncommutative extended systems and it contains, as a particular…
We revisit the old question of what distinguishes the formulation of spacetime geometry in terms of a Lorentzian metric physically from more general geometric structures. Our approach to this question is operational and leads us to also…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of…
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…
We develop a theory of Lp spaces based on outer measures rather than measures. This theory includes the classical Lp theory on measure spaces as special case. It also covers parts of potential theory and Carleson embedding theorems. The…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically,…
We present a novel approach to computing transition probabilities in quantum field theory, which allows them to be written directly in terms of expectation values of nested commutators and anti-commutators of field operators, rather than…