This is not a disproof of the quantum PCP conjecture! In this note we use perturbation on the commuting Hamiltonian problem on a graph, based on results by Bravyi and Vyalyi, to provide a partial no-go theorem for quantum PCP. Specifically, we derive an upper bound on how large the promise gap can be for the quantum PCP still to hold, as a function of the non-commuteness of the system. As the s...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

The set of all centralizers elements in a finite group G is denoted by Cent(G) and called n-centralizer if |Cent(G)|=n. In this paper, the structure non-abelian with property that GZ(G)≅Zp2⋊Zp2 obtained. As consequence, it proved such has exactly [(p+1)2+1] element commuting conjugacy class graph completely determined.

Suppose G be a finite group and X subset of G. The commuting graph, denoted by C(G,X), is simple undirected where ⊂G being the set vertex two distinct vertices x,y∈X are joined an edge if only xy = yx. aim this paper was to describe structure disconnected graph considering symplectic conjugacy class elements order three. main work discover disc diameter subgraph as well suborbits groups S4(2)',...

Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...

In this paper we study bipartite quantum correlations using techniques from tracial polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a qua...

Kanishka Bhaduri Netflix Inc. 100 Winchester Cir. Los Gatos, CA, 95032 United States Tel.: 408 540 3331 (office) E-mail: [email protected] Abstract An automatic service to match commuting trips has been designed. Candidate carpoolers register their personal profile and a set of periodically recurring trips. The Global CarPooling Matching Service (GCPMS) shall advise registered candidates ho...