We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters of an unknown Gaussian process, considering a noisy source of radiation the phase of which is not locked to the pump of the process. We verify the sufficiency of passive optical elements in the interferometer, active optical elements do not improve the quality of the estimation. We also prove the robustness of the method against the noise and loss in both interferometric channels and the sample. The proposed method is suitable even for the case when a source of radiation sufficient for homodyne detection is not available.

Department of Optics Palacky University 17 listopadu 12 771 46 Olomouc Czech Republic

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Glauber R. J. Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963).

Grangier P., Roger G. & Aspect A. Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. Europhys. Lett. 1, 173 (1986).

Hong C. K., Ou Z. Y. & Mandel L. Measurement of subpicosecond time intervals between two photons by interference Phys. Rev. Lett. 59, 2044 (1987). PubMed

Ježek M. et al.. Experimental test of the quantum non-Gaussian character of a heralded single-photon state. Phys. Rev. Lett. 107, 213602 (2011). PubMed

Nothaft M. et al.. Electrically driven photon antibunching from a single molecule at room temperature. Nature Comm. 3, 628 (2011). PubMed

Wientjes E., Renger J., Curto A. G., Cogdell R. & van Hulst N. F. Strong antenna-enhanced fluorescence of a single light-harvesting complex shows photon antibunching. Nature Comm. 5, 4236 (2014). PubMed PMC

Koperski M. et al.. Single photon emitters in exfoliated WSe2 structures, Nature Nanotech. 10, 503–506 (2015). PubMed

Ma X., Hartmann N. F., Baldwin J. K. S., Doorn S. K. & Htoon H. Room-temperature single-photon generation from solitary dopants of carbon nanotubes. Nature Nanotech. 10, 671–675 (2015). PubMed

Lang C. et al.. Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies. Nature Phys. 9, 345–348 (2013).

Silverstone J. W. et al.. On-chip quantum interference between silicon photon-pair sources. Nature Phot. 8, 104–108 (2014).

Gschrey M. et al.. Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography. Nature Comm. 6, 7662 (2015). PubMed PMC

Somaschi N. et al.. Near-optimal single-photon sources in the solid state, Nature Phot. 10, 340–345 (2016).

Breitenbach G., Schiller S. & Mlynek J. Measurement of the quantum states of squeezed light, Nature 387, 471–475 (1997).

Andersen U. L., Gehring T., Marquardt Ch. & Leuchs G. 30 years of squeezed light generation, Phys. Scr. 91, 053001 (2016).

Born M. & Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

Mandel L. & Wolf E. Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Eberle T. et al.. Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection, Phys. Rev. Lett. 104, 251102 (2010). PubMed

Mehmet M. et al.. Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB. Opt. Exp. 19, 25763 (2011). PubMed

Laiho K., Cassemiro K. N., Gross D. & Silberhorn Ch. Probing the negative Wigner function of a pulsed single photon point by point, Phys. Rev. Lett. 105, 253603 (2010). PubMed

Harder G. et al.. Local sampling of the Wigner function at telecom wavelength with loss-tolerant detection of photon statistics. Phys. Rev. Lett. 116, 133601 (2016). PubMed

Slusher R., Hollberg L., Yurke B., Mertz J. & Valley J. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett. 55, 2409 (1985). PubMed

Wu L. A., Kimble H. J., Hall J. L. & Wu H. Generation of squeezed states by parametric down conversion, Phys. Rev. Lett. 57, 2520 (1986). PubMed

Shelby R. M., Levenson M. D., Walls D. F., Aspect A. & Milburn G. J. Generation of squeezed states of light with a fiber-optic ring interferometer, Phys. Rev. A 33, 4008 (1986). PubMed

Ourjoumtsev A. et al.. Observation of squeezed light from one atom excited with two photons. Nature 474, 623–626 (2011). PubMed

Schulte C. H. H. et al.. Quadrature squeezed photons from a two-level system, Nature 525, 222 (2015). PubMed

Safavi-Naeini A. H. et al.. Squeezed light from a silicon micromechanical resonator, Nature 500, 185–189 (2013). PubMed

Wollman E. E. et al.. Quantum squeezing of motion in a mechanical resonator, Science 349, 952 (2015). PubMed

Castellanos-Beltran M. A., Irwin K. D., Hilton G. C., Vale L. R. & Lehnert K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008).

Milburn G. J., Chen W.-Y. & Jones K. R. Hyperbolic phase and squeeze-parameter estimation. Phys. Rev. A 50, 801 (1994). PubMed

Chiribella G., D’Ariano G. M. & Sacchi M. F. Optimal estimation of squeezing. Phys. Rev. A 73, 062103 (2006).

Gaiba R. & Paris M. G. Squeezed vacuum as a universal quantum probe, Phys. Lett. A 373, 934–939 (2009).

Šafránek D., Lee A. R. & Fuentes I. Quantum parameter estimation using multi-mode Gaussian states, New J. Phys. 17, 073016 (2015).

Šafránek D. & Fuentes I. Optimal probe states for the estimation of Gaussian unitary channels, http://arxiv.org/abs/1603.05545 (2016).

Pinel O., Jian P., Treps N., Fabre C. & Braun D. Quantum parameter estimation using general single-mode Gaussian states. Phys. Rev. A 88, 040102(R) (2013).

Fiurášek J. Continuous-variable quantum process tomography with squeezed-state probes, Phys. Rev. A 92, 022101 (2015).

Sparaciari C., Olivares S. & Paris M. G. Gaussian state interferometry with passive and active elements, Phys. Rev. A 93, 023810 (2016).

Adesso G. Gaussian interferometric power, Phys. Rev. A 90, 022321 (2014).

Ruppert L., Usenko V. C. & Filip R. Estimation of the covariance matrix of macroscopic quantum states, Phys. Rev. A 93, 052114 (2016).

Usenko V. C., Ruppert L. & Filip R. Quantum communication with macroscopically bright nonclassical states, Opt. Exp. 23, 31534–31543 (2015). PubMed

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