Related papers: Remote state preparation in higher dimension and t…

We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic…

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general very hard, we show that the following…

A Hilbert space frame on $R^n$ is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic questions here which have never been answered in any $R^n$:…

For every pattern $P$, consisting of a finite set of points in the plane, $S_{P}(n,m)$ is defined as the largest number of similar copies of $P$ among sets of $n$ points in the plane without $m$ points on a line. A general construction,…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

This paper studies spatial capacity in a stochastic wireless ad hoc network, where multi-stage probing and data transmission are sequentially performed. We propose a novel signal-to-interference-ratio (SIR) threshold based scheduling…

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…

Sliced optimal transport, which is basically a Radon transform followed by one-dimensional optimal transport, became popular in various applications due to its efficient computation. In this paper, we deal with sliced optimal transport on…

A homemorphism between domains in $\mathbb R^n$, $n\ge 2$ is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purely metric quantity -- is uniformly bounded. Gehring proved…

Structural physical approximation (SPA) has been exploited to approximate non-physical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of…

We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold Sym$^N(T^4)$ to all orders in $N$. This allows us to compute how 1/4-BPS states of the D1-D5 system on $AdS_3\times S^3\times T^4$ are…

In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…

Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…

Deterministic preparation of high-excitation Fock states is a central challenge in bosonic quantum information, with control complexity that generically explodes as the Hilbert space dimension grows. Here we introduce resonant subspace…

We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…

Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom…

We present a performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation. This addresses a problem arising when one seeks solutions to…

We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative…