Related papers: The LU-LC conjecture, diagonal local operations an…
We propose a new kind of invariant of multi-party stabilizer states with respect to local Clifford equivalence. These homological invariants are discrete entities defined in terms of the entanglement a state enjoys with respect to arbitrary…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
Entanglement, as studied in quantum information science, and non-local quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
The study of state transformations under local operations and classical communication (LOCC) plays a crucial role in entanglement theory. While this has been long ago characterized for pure bipartite states, the situation is drastically…
The stabilizer group of an n-qubit state \psi is the set of all matrices of the form g=g_1\otimes\cdots\otimes g_n, with g_1,...,g_n being any 2x2 invertible complex matrices, that satisfy g\psi=\psi. We show that for 5 or more qubits,…
We adopt a resource-theoretic framework to classify different types of quantum network nonlocality in terms of operational constraints placed on the network. One type of constraint limits the parties to perform local Clifford gates on pure…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…
Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise…
In a previous paper we formulated an analogue of the Ichino-Ikeda conjectures for Whittaker-Fourier coefficients of cusp forms on quasi-split groups, as well as the metaplectic group of arbitrary rank. In this paper we reduce the conjecture…
We define, for a locally compact quantum group $G$ in the sense of Kustermans--Vaes, the space of $LUC(G)$ of left uniformly continuous elements in $L^\infty(G)$. This definition covers both the usual left uniformly continuous functions on…
Localized unitary operators are basic probes of locality and causality in quantum systems: localized unitary operators create localized excitations in entangled states. Working with an explicit form, we explore the properties of these…
One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed by using the stabilizer operators of some given…
We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom,…
Inspired by work of McMullen, we show that any orbit of the diagonal group in the space of lattices accumulates on the set of stable lattices. As consequences, we settle a conjecture of Ramharter concerning the asymptotic behaviour of the…
It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…
Inspired by work of McMullen, we show that any orbit for the action of the diagonal group on the space of lattices, accumulates on a stable lattice. We use this to settle a conjecture of Ramharter about Mordell's constant, get new proofs of…
A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…
We show that the classification of bi-partite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this…