Deterministic tripartite sharing of eight restricted sets of single-qubit operations with two Bell states or a GHZ state

Abstract

Two tripartite schemes with a pair of Bell states and a Greenberger-Horne-Zeilinger (GHZ) state respectively have been proposed recently by Zhang and Cheung for remotely sharing two restricted sets of operations in a deterministic manner [J. Phys. B 44 (2011) 165508]. In this paper, we generalize the schemes with the same quantum channels so that another six restricted sets of operations can be shared deterministically, too. Features about scheme security, sharer symmetry, ful¯llment determinacy and experimental feasibility are discussed and revealed. Moreover, some comparisons are also made from the aspects of quantum and classical resource consumption, necessary operation complexity and e±ciency.

Four-party deterministic quantum operation sharing with a generalized seven-qubit Brown state

“…Shared entanglements are indispensable in QOS [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In all existing QOS schemes, some multi-particle entangled states, such as Bell and GHZ states [25,37], W states [29,31], cluster states [30,32], genuine states [26,38] and so on, have been employed as quantum channels to fulfill QOS.…”

“…Shared entanglements are indispensable in QOS [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In all existing QOS schemes, some multi-particle entangled states, such as Bell and GHZ states [25,37], W states [29,31], cluster states [30,32], genuine states [26,38] and so on, have been employed as quantum channels to fulfill QOS. In 2005, Brown et al [39] creatively presented and deeply studied a fivequbit state by means of the computationally tractable entanglement measure developed by themselves and found that it is more highly entangled than a five-qubit GHZ state.…”

Remotely Sharing a Single-Qubit Operation via a Six-Qubit Entangled State

“…The basic idea of quantum operation sharing in a simplest case is that, with shared entanglement and local operations and classical communications (LOCC) the initial performer of a singlequbit operation can assure the operation be finally performed on a remote target's qubit in a agent's site if and only if both agents cooperate [25]. Recently, some QOS schemes have been devised by using different entangled states [25][26][27][28][29][30][31].…”