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arXiv:2211.12992 · Physical Review A

Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state

Célia Griffet, Matthieu Arnhem, Stephan De Bièvre, Nicolas J. Cerf

Published Aug 31, 2023• 5 citations
arXivHTMLPDF

Abstract

Assessing whether a quantum state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ is nonclassical (i.e., incompatible with a mixture of coherent states) is a ubiquitous question in quantum optics, yet a nontrivial experimental task because many nonclassicality witnesses are nonlinear in $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$. In particular, if we want to witness or measure the nonclassicality of a state by evaluating its quadrature coherence scale, this a priori requires full state tomography. Here, we provide an experimental procedure for directly accessing this quantity with a simple linear interferometer involving two replicas (independent and identical copies) of the state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ supplemented with photon-number-resolving measurements. This finding, which we interpret as an extension of the Hong-Ou-Mandel effect, illustrates the wide applicability of the multicopy interferometric technique in order to circumvent state tomography in quantum optics.

DOI
10.1103/physreva.108.023730

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Assessing whether a quantum state \ensuremathρ\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}\ensuremathρ\ifmmode^\elseˆ\fi​ is nonclassical (i.e., incompatible with a mixture of coherent states) is a ubiquitous question in quantum optics, yet a nontrivial experimental task because many nonclassicality witnesses are nonlinear in \ensuremathρ\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}\ensuremathρ\ifmmode^\elseˆ\fi​. In particular, if we want to witness or measure the nonclassicality of a state by evaluating its quadrature coherence scale, this a priori requires full state tomography. Here, we provide an experimental procedure for directly accessing this quantity with a simple linear interferometer involving two replicas (independent and identical copies) of the state \ensuremathρ\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}\ensuremathρ\ifmmode^\elseˆ\fi​ supplemented with photon-number-resolving measurements. This finding, which we interpret as an extension of the Hong-Ou-Mandel effect, illustrates the wide applicability of the multicopy interferometric technique in order to circumvent state tomography in quantum optics.
Distinguishing quantum states that admit a classical counterpart from those that exhibit nonclassicality has long been a central issue in quantum optics. Finding an implementable criterion certifying optical nonclassicality (i.e., the incompatibility with a statistical mixture of coherent states) is of major importance as it often is a prerequisite to quantum information processes. A hierarchy of conditions for detecting whether a quantum state exhibits optical nonclassicality can be written based on matrices of moments of the optical field [E. V. Shchukin and W. Vogel, Phys. Rev. A 72, 043808 (2005)]. Here, we design optical nonclassicality observables that act on several replicas of a quantum state and whose expectation value coincides with the determinant of these matrices, hence providing witnesses of optical nonclassicality that overcome the need for state tomography. These multicopy observables are used to construct a family of physically implementable schemes involving linear optical operations and photon number detectors.
Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation.Finding reliable and effective methods for assessing its presence is then highly desirable.Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis.Here, we experimentally measure a type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way.Our experiment uses a single interferometric setup to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests.Aside from coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness.Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.
We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of nine Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate both that these invariants are a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity FindF_{\mathrm{ind}}Find​ of an NNN-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on FindF_{\mathrm{ind}}Find​. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of FindF_{\mathrm{ind}}Find​ for arbitrary NNN-photon states. Both protocols can certify Find=1−O(ε)F_{\mathrm{ind}} = 1 - \mathcal{O}(ε)Find​=1−O(ε) using provably optimal O(1/ε)\mathcal{O}(1/ε)O(1/ε) samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.
We propose a methodology to emulate quantum phenomena arising from any nonclassical quantum state using only a finite set of mixtures of coherent states. This allows us to successfully reproduce well-known quantum effects using resources that can be much more feasibly generated in the laboratory. We present a simple procedure to experimentally carry out quantum-state emulation with coherent states, illustrate it emulating multiphoton NOON states with few phase-averaged coherent states, and demonstrate its capabilities in observing fundamental quantum mechanical effects, such as the Hong-Ou-Mandel effect, violating Bell inequalities and witnessing quantum nonclassicality.