Sufficient condition for a quantum state to be genuinely quantum non-Gaussian
We show that the expectation value of the operator $\hat{{ \mathcal O }}\equiv \exp (-c{\hat{x}}^{2})+\exp (-c{\hat{p}}^{2})$ defined by the position and momentum operators $\hat{x}$ and $\hat{p}$ with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaac25 |
| Summary: | We show that the expectation value of the operator $\hat{{ \mathcal O }}\equiv \exp (-c{\hat{x}}^{2})+\exp (-c{\hat{p}}^{2})$ defined by the position and momentum operators $\hat{x}$ and $\hat{p}$ with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation. |
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| ISSN: | 1367-2630 |