Related papers: Lower Bounds on Coherent State Rank
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…
We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large…
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or…
We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
A coherent state is defined conventionally in different ways such as a displaced vacuum state, an eigenket of annihilation operator or as an infinite dimensional Poissonian superposition of Fock states. In this work, we describe a…
Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for…
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
We prove new upper and lower bounds on $\epsilon$-approximate sign-rank, a relaxation of sign-rank introduced by Chornomaz, Moran, and Waknine (STOC 2025). We show that every $m \times n$ sign matrix with approximate sign-rank $d$ contains…
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a new construction of inner- and outer-bounding polytopes…
The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization,…
We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix by a…
In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states $\{\ket{\alpha, \beta}\ |\ \alpha, \beta \in…
The low-rank matrix optimization with affine set (rank-MOA) is to minimize a continuously differentiable function over a low-rank set intersecting with an affine set. Under some suitable assumptions, the intersection rule of the Fr\'{e}chet…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states; (iii) output states of dense…