Certification of stellar ranks of quantum states of light with a pair of click detectors

Abstract

Stellar rank of quantum state of light quantifes the amount of non-Gaussian resources required for its generation. One popular and practical approach to certification of stellar rank is based on measurement of click statistics with an array of binary detectors that can only distinguish the presence and absence of photons. Specifically, it was shown that measurements with an array of m+1 detectors allow one to certify stellar rank m of approximate Fock state $|m⟩$, even when the state is subjected to losses or certain noise. Here we address the question as to how many click detectors are in principle required to certify stellar ranks higher than one. We show that two click detectors arranged in a Hanbury Brown-Twiss setup suffice. Interestingly, detection of stellar ranks higher than one is greatly facilitated by making the total detection efficiency of the detectors sufficiently low but well calibrated. Losses affect the response of the detection scheme in a way that can be exploited to certify stellar rank of higher Fock states. We explicitly construct the corresponding stellar rank witnesses and discuss dependence of the stellar rank thresholds on parameters of the considered setup. Our results reveal that it is possible to certify stellar ranks higher than 1 even with a minimalistic scheme that provides only very coarse-grained information about the photon number statistics of the characterized state.

12 pages, 5 figures, REVTeX4, final version accepted for publication in Phys. Rev. A

References in corpus (30)

• Entanglement detection
• Generation of a superposition of odd photon number states for quantum information networks
• Photon number resolution using a time-multiplexed single-photon detector
• Non-Gaussian Quantum States and Where to Find Them
• Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
• Generating superposition of up-to three photons for continuous variable quantum information processing
• Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
• Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources
• Optical continuous-variable qubit
• Experimental generation of multi-photon Fock states
• Non-Gaussianity of quantum states: an experimental test on single-photon added coherent states
• Certification of non-Gaussian states with operational measurements
• Measurement-induced strong Kerr nonlinearity for weak quantum states of light
• Revealing nonclassicality beyond Gaussian states via a single marginal distribution
• Experimental preparation of multiphoton-added coherent states of light
• Quantum non-Gaussianity of light and atoms
• Nonlinear squeezing for measurement-based non-Gaussian operations in time domain
• Photon-by-photon quantum light state engineering
• Quantum non-Gaussianity of multi-phonon states of a single atom
• Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator
• Efficient construction of witnesses of stellar rank of nonclassical states of light
• Generation of Highly Pure Single-Photon State at Telecommunication Wavelength
• Ground state nature and nonlinear squeezing of Gottesman-Kitaev-Preskill states
• Experimental demonstration of a versatile and scalable scheme for iterative generation of non-Gaussian states of light
• Quantum non-Gaussianity from a large ensemble of single photon emitters
• Hierarchical Verification of Non-Gaussian Coherence in Bosonic Quantum States
• Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state
• Experimental retrieval of photon statistics from click detection
• High-resolution coincidence counting system for large-scale photonics applications
• Generalized squeezing as a witness