Complete and Nondestructive Atomic Greenberger–Horne–Zeilinger‐State Analysis Assisted by Invariant‐Based Inverse Engineering

Abstract

A protocol to realize complete and nondestructive atomic Greenberger-Horne-Zeilinger (GHZ)-state analysis in cavity quantum electrodynamics (QED) systems is presented. In this protocol, the three information-carrier atoms and the three auxiliary atoms are trapped in six separated cavities, respectively. After ten-step operations, the information for distinguishing the eight different GHZ states of the three information-carrier atoms is encoded on the auxiliary atoms. Thus, by means of detecting the auxiliary atoms, complete and nondestructive GHZ-state analysis with high success probability is realized. Moreover, the driving pluses of operations are designed as a simple superposition of Gaussian or trigonometric functions by using the invariant-based inverse engineering. Therefore, the protocol can be realized experimentally and applied in some quantum information tasks based on complete GHZ-state analysis with less physical entanglement resource.interesting protocol for complete and nondestructive Bell-state analysis for two superconducting quantum interference device qubits. In protocols, [36,37] different Bell states can be distinguished completely with high success probabilities.On the other hand, GHZ state plays a crucial part in testing quantum mechanics against local hidden theory without Bell inequality. [47] Besides, the information capacity of GHZ states is bigger than Bell states, which makes GHZ states more promising than Bell states in multiparticle systems. Thus, finding an efficient and feasible way to realize GHZ-state analysis is an essential issue of QIP. For example, in 2005, Jin et al. [48] have presented a protocol to teleport an unknown atomic entangled state in driving cavity quantum electrodynamics (QED) systems. In this protocol, one important step is to distinguish different GHZ states of three atoms.Actually, as early as 1998, Pan et al. [49] have put forward a groundbreaking protocol to structure a GHZ-state analyzer by using linear-optics elements. The GHZ-state analyzer could distinguish two of the eight maximally entangled GHZ states, which signified that the measurement would be probabilistic. In order to overcome the nondeterminacy of detection, in 2005, Qian et al. [50] have proposed an innovative protocol for a three-particle GHZ-state analyzer using quantum nondemolition parity detectors based on the cross-Kerr nonlinearity and linear-optics elements. In protocol, [50] all GHZ states can be discriminated with nearly unity probability. But, the GHZ states will be destructed after analyzing. Obviously, nondestructive GHZ-state analysis can save the physical entanglement resource and boost the efficiency of QIP. Thus, how to carry out a complete and nondestructive GHZ-state analysis becomes a significant problem. To solve the problem, in 2012, Su et al. [51] have presented a protocol for completely and nondestructively distinguishing Bell states and GHZ states by employing simplified symmetry analyzer. In 2013, Wei et al. [52] have proposed a protocol for the complete and nondestr...

Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits

“…In particular, maximally-entangled multiqubit states of W - [2] and GHZ [3] type are of both conceptual and practical importance in the realm of quantum-information processing (QIP) [4]. Owing to their already proven usefulness in QIP [5,6], a large number of schemes for the preparation of W [7][8][9][10][11][12][13][14][15] and GHZ states [16][17][18][19][20][21] in various physical platforms have been proposed in recent years. Among those platforms, one of the most promising ones from the standpoint of large-scale quantum computing and analog quantum simulation, is based on ensembles of neutral atoms in Rydberg states [22][23][24][25].…”

Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control

“…In particular, in the three-qubit case W and GHZ are the only two subclasses of states with genuine tripartite entanglement [6]. Both classes have proven useful in diverse QIP contexts [7][8][9][10][11], which was the primary motivation behind a large number of proposals for the efficient preparation of W [12][13][14][15][16][17][18][19][20][21] and GHZ states [22][23][24][25][26][27][28][29][30] in various physical systems.…”

Dynamical generation of chiral $W$ and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers

“…Two particularly prominent classes of such states are W [2] and GHZ [3] states, for which it is known that they cannot be transformed into each other through local operations and classical communication (LOCC inequivalence [1]). Owing to their demonstrated usefulness in various QIP protocols [4,5], a multitude of different schemes for the preparation of W [6][7][8][9][10][11][12][13][14][15] and GHZ states [16][17][18][19][20] in various physical platforms have been proposed in recent years.…”