Related papers: Bounds on entanglement dimensions and quantum grap…
The future progress of semi-device independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite dimensional quantum resources. In this work, we…
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
Understanding the relationship between various different forms of nonclassicality and their resource character is of great importance in quantum foundation and quantum information. Here, we discuss a quantitative link between quantum…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
The smallest eigenvalues of (distance-j) Hamming graphs with distance parameter j at least half the length were completely determined by Brouwer et al. (2018). In the present work, we address the complementary regime, namely distances j…
We derive a family of optimal protocols, in the sense of saturating the quantum Cram\'{e}r-Rao bound, for measuring a linear combination of $d$ field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor…
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…
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…
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as, for instance, quantum communication, quantum computing, and quantum interferometry.…
Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By…
For a simple graph, the minimum rank problem is to determine the smallest rank among the symmetric matrices whose off-diagonal nonzero entries occur in positions corresponding to the edges of the graph. Bounds on this minimum rank (and on…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP…