Given a bipartite graph with bipartition (A,B) where B is equipartitioned into k blocks, can the vertices in A be picked one by so that at every step, cover roughly same number of each these blocks? We show that, if block has cardinality m, have degree, and vertex most cm neighbors c>0 small constant, then there an ordering v1,…,vn such for j∈{1,…,n}, numbers neighbor {v1,…,vj} two blocks diffe...

How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question constructing an entanglement witness based on photon detections preceded displacement operations to reveal genuine entanglement. Our is defined as sum three observables that measured locally and assessed with two measurement settings for any number parties ...

We study how the number of employed modes impacts ability to witness non-Markovian evolutions via correlation backflows in continuous-variable quantum dynamics. first prove existence Gaussian that do not show any revivals correlations between mode evolving through dynamics and a single ancillary mode. then demonstrate this scenario radically changes when two are considered. Indeed, we same can ...

Abstract Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain in every bipartition and as such can be regarded a valuable resource protocols quantum information processing. A recent direction research construction genuinely subspaces (GESs)—the class consisting entirely states. In this paper we present methods including those maximal p...

We study the quantum correlations embedded in open Rabi systems. Specifically, we how correlation depends on coupling strength, number of qubits, and reservoir temperatures. numerically calculate up to three qubits interacting with a single field mode. find that exhibit maximum for given which inversely subsystems temperature. explore this feature affects performance many-qubit Otto heat engine...

A bipartite graph is called bipancyclic if it contains cycles of every even length from four up to the number vertices in graph. theorem Schmeichel and Mitchem states that for $n \geqslant 4$, balanced on $2n$ which each vertex one color class has degree greater than $\frac{n}{2}$ other at least bipancyclic. We prove a generalization this setting transversals. Namely, we show given family $\mat...

Given a statistical ensemble of quantum states, the corresponding Page curve quantifies average entanglement entropy associated with each possible spatial bipartition system. In this work, we study natural extension in presence conservation law and introduce symmetry-resolved curves, characterizing bipartite entropies. We derive explicit analytic formulas for two important ensembles $U(1)$-symm...

Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition subsystems. As difficulty problem, most results are restricted to tripartite systems. Here we consider a weaker form called local dis...

We study purity decay -- a measure of bipartite entanglement in chain $n$ qubits under the action various geometries nearest-neighbor random two-site unitary gates. use Markov description average evolution, using further reduction to obtain transfer matrix only polynomial dimension $n$. In most circuits, an exception being brick-wall configuration, decays its asymptotic value two stages: initia...

Many classical partitioning problems in combinatorics ask for a single quantity to be maximized or minimized over a set of partitions of a combinatorial object. For instance, Max Cut asks for the largest bipartite subgraph of a graphG, while Min Bisection asks for the minimum size of a cut into two equal pieces. In judicious partitioning problems, we seek to maximize or minimize a number of qua...