相关论文: Semidefinite relaxations for high-dimensional enta…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates continues to be a great challenge…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective…
The coefficient matrix is an efficient tool in entanglement classification under stochastic local operation and classical communication. In this work, we take all the ranks of the coefficient matrices into account in the method of…
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a…
Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank,…
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement…
We investigate the hypercube networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the…
The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect…
We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n…
Multipartite entanglement is the key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies…
Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and…
Quantum entanglement lies at the heart in quantum information processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available…
We quantify the one-shot entanglement cost of an arbitrary bipartite state, that is the minimum number of singlets needed by two distant parties to create a single copy of the state up to a finite accuracy, using local operations and…
Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow to exclude arbitrary LHS models, it may…
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…
We present a unified framework for multipartite entanglement characterization based on the conditional gradient (CG) method, incorporating both fast heuristic detection and rigorous witness construction with numerical error control. Our…