Multipartite entanglement states of higher uniformity

Shanqi Pang, Zhang Xiao, Jiao Du, Tian‐Yin Wang

2020Journal of Physics A Mathematical and Theoretical19 citationsDOI

Abstract

Abstract In this study, we provide a positive answer to the problem of whether N -qubit pure quantum states exist in which all k -body reduced density are maximally mixed for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mo><</mml:mo> <mml:mrow> <mml:mo>⌊</mml:mo> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:mo>⌋</mml:mo> </mml:mrow> </mml:math> in [1]. In addition, for k ⩾ 4 and any d , there exists an integer N 0 ( k , d ) such that whenever N ⩾ N 0 ( k , d ), we can construct a series of infinite classes of k -uniform states of N qudits with any level d , including infinitely many absolutely maximally entangled states.

Topics & Concepts

Quantum entanglementMultipartite entanglementMultipartiteStatistical physicsQuantum mechanicsComputer sciencePhysicsSquashed entanglementQuantumQuantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications