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arXiv:quant-ph/0204049 · Chinese Physics Letters

Experimentally Obtaining the Likeness of Two Unknown Qubits on a Nuclear-Magnetic-Resonance Quantum Information Processor

Xue Fei, Du Jiang-Feng, Zhou Xian-Yi, Rongdian Han, Jihui Wu

Published Sep 24, 2003• 7 citations
arXivHTMLPDF

Abstract

We study the discrimination of quantum states from the other way around, i.e. the likeness of two quantum states. The fidelity is used to describe the likeness of two quantum states. Then we present a scheme to obtain the fidelity of two unknown qubits directly from the integral area of the spectra of the assistant qubit (spin) on a nuclear-magnetic-resonance quantum information processor. Finally, we demonstrate the scheme on a three-qubit quantum information processor. The experimental data are consistent with the theoretical expectation with an average error of 0.05, which confirms the scheme.

DOI
10.1088/0256-307x/20/10/304

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We study the discrimination of quantum states from the other way around, i.e. the likeness of two quantum states. The fidelity is used to describe the likeness of two quantum states. Then we present a scheme to obtain the fidelity of two unknown qubits directly from the integral area of the spectra of the assistant qubit (spin) on a nuclear-magnetic-resonance quantum information processor. Finally, we demonstrate the scheme on a three-qubit quantum information processor. The experimental data are consistent with the theoretical expectation with an average error of 0.05, which confirms the scheme.
We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and WWW-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and WWW states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and WWW states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the WWW state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.
Superposition, arguably the most fundamental property of quantum mechanics, lies at the heart of quantum information science. However, how to create the superposition of any two unknown pure states remains as a daunting challenge. Recently, it was proved that such a quantum protocol does not exist if the two input states are completely unknown, whereas a probabilistic protocol is still available with some prior knowledge about the input states [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)]. The knowledge is that both of the two input states have nonzero overlaps with some given referential state. In this work, we experimentally realize the probabilistic protocol of superposing two pure states in a three-qubit nuclear magnetic resonance system. We demonstrate the feasibility of the protocol by preparing a families of input states, and the average fidelity between the prepared state and expected superposition state is over 99%. Moreover, we experimentally illustrate the limitation of the protocol that it is likely to fail or yields very low fidelity, if the nonzero overlaps are approaching zero. Our experimental implementation can be extended to more complex situations and other quantum systems.
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We experimentally demonstrate the efficacy of a three-layer nested Uhrig dynamical decoupling (NUDD) sequence to preserve arbitrary quantum states in a two-dimensional subspace of the four-dimensional two-qubit Hilbert space on a nuclear magnetic resonance quantum information processor. The effect of the state preservation is studied first on four known states, including two product states and two maximally entangled Bell states. Next, to evaluate the preservation capacity of the NUDD scheme, we apply it to eight randomly generated states in the subspace. Although, the preservation of different states varies, the scheme, on the average, performs very well. The complete tomographs of the states at different time points are used to compute fidelity. State fidelities using NUDD protection are compared with those obtained without using any protection. The nested pulse schemes are complex in nature and require careful experimental implementation.