Proposal for generating and detecting multi-qubit GHZ states in circuit QED

Lev S Bishop,A Nunnenkamp,E Ginossar,R J Schoelkopf,D Price,L Tornberg,A A Houck,G Johansson,Jens Koch,J M Gambetta,S M Girvin

doi:10.1088/1367-2630/11/7/073040

Lev S Bishop, A Nunnenkamp + Show 9 more

Open Access

https://doi.org/10.1088/1367-2630/11/7/073040

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Abstract

We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.

Highlights

We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics
We have presented a concrete proposal for efficient statistical production of multiqubit GHZ states by dispersive measurement in a cQED setup, taking into account the realistic conditions of decoherence and decay
By using the global dispersive measurement in the same setup, we have proposed a scheme for implementing parity measurements on the prepared state

Summary

Idealized preparation and detection of GHZ states

J =1 j =1 where |· j denotes the state of qubit number j. The beauty of the GHZ state lies in the fact that, in principle, violation of classicality can be proven with a single measurement of the corresponding Bell–Mermin operator M [23], see (4). This has to be contrasted with the situation of the two-qubit CHSH scheme [29, 30], where such a proof necessarily requires accumulating statistics. Key to this difference is the property of the GHZ state being an eigenstate of M and simultaneously of the measurable parity operators which sum up to M. We turn to the full discussion of the realistic situation including these effects

Preparation scheme

Detection scheme

Preparation of the GHZ state under realistic conditions

Boxcar filter

GHZ state detection under realistic conditions

Conclusions