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arXiv:1903.03526 · Physical Review Research

General mapping of multiqudit entanglement conditions to nonseparability indicators for quantum-optical fields

Junghee Ryu, Bianka Woloncewicz, Marcin Marciniak, Marcin Wieśniak, Marek Żukowski

Published Dec 19, 2019• 5 citations
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Abstract

A method is given to transform any multi-qubit entanglement witness into an entanglement indicator for optical fields. This approach can be useful in situations where intensity correlations are measured, and for states for which photon numbers are undefined. When one moves to run-by-run correlations of intensity rates (intensities at a given detector divided by the total locally observed intensity at all detectors at a given station) the approach allows to transform any qudit Bell inequality into a Bell inequality for quantum optical fields.

DOI
10.1103/physrevresearch.1.032041

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A method is given to transform any multi-qubit entanglement witness into an entanglement indicator for optical fields. This approach can be useful in situations where intensity correlations are measured, and for states for which photon numbers are undefined. When one moves to run-by-run correlations of intensity rates (intensities at a given detector divided by the total locally observed intensity at all detectors at a given station) the approach allows to transform any qudit Bell inequality into a Bell inequality for quantum optical fields.
Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as, e.g., for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows one to vastly expand the family of such indicators.
Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers.For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum.It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach.The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail.Here we show an extension of this approach beyond phenomena linked with polarization.We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state.EPR-inspired entanglement conditions for all prime numbers of modes are presented.The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.
Abstract We generalize a new approach to entanglement conditions for light of undefined photons numbers given in Żukowski et al (2017 Phys. Rev. A 95 042113) for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one to perform experiments based upon multiport beamsplitters. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into modes (beams), one can have perfect EPR-like correlations of numbers of photons emitted into ‘conjugate modes’ which can be monitored at spatially separated detection stations. We provide entanglement conditions for experiments involving three modes on each side, and three-input-three-output multiport beamsplitters, and show their violations by bright squeezed vacuum states. We show that a condition expressed in terms of averages of observed rates is a much better entanglement indicator than a related one for the usual intensity variables. Thus, the rates seem to emerge as a powerful concept in quantum optics, especially for fields of undefined intensities.
Integrated optics allows one to perform interferometric experiments based upon multi-port beam-splitter. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into (beams), one can have perfect EPR-like correlations of numbers of photons emitted into conjugate modes which can be monitored at spatially separated detection stations. We provide series of entanglement conditions for all prime numbers of modes, and show their violations by bright multi-mode squeezed vacuum states. One family of such conditions is given in terms of the usual intensity-related variables. Moreover, we show that an alternative series of conditions expressed in terms averages of observed rates, which is a generalization of the ones given in arXiv:1508.02368, is a much better entanglement indicator. Thus the rates seem to emerge as a powerful concept in quantum optics. Generalizations of the approach are expected.
Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.