Lower bounds for the fidelity of entangled state preparation

Abstract

Estimating the fidelity of state preparation in multi-qubit systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this paper we give simple expressions to estimate the fidelity of multi-qubit state preparation for rotational-invariant, stabilizer, and generalized coherent states. We specifically discuss the cat, W-type, and generalized coherent states, and obtain efficiently measurable lower bounds for the fidelity. We use these techniques to estimate the fidelity of a quantum simulation of an Ising-like interacting model using two trapped ions. These results are directly applicable to experiments using fidelity-based entanglement witnesses, such as quantum simulations and quantum computation.

arXiv comment8 pages, 2 figures. Added discussion about rotational-invariant states

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• Geometry of faithful entanglement
• Statistically significant tests of multiparticle quantum correlations based on randomized measurements
• Optimal error intervals for properties of the quantum state
• Cubic nonlinear squeezing and its decoherence
• Quantum circuit synthesis for generalized coherent states
• Scalable Experimental Bounds for Entangled Quantum State Fidelities