研究目的
Investigating quantum nonlocality in bipartite scenarios with three ternary-outcome measurements, exploring new facet-defining Bell inequalities, their quantum violations, and experimental demonstrations using entangled photon pairs.
研究成果
The study presents new facet-defining Bell inequalities for the {[3,3,3],[3,3,3]} scenario, showing that maximal quantum violations can be achieved with two-qubit states, challenging the assumption that Hilbert space dimension must match measurement outcomes. One inequality requires non-projective measurements for maximal violation in the qubit subspace. Experimental demonstrations with entangled photon pairs confirm violations, and device-independent-inspired analysis allows entanglement estimation from raw data, though signaling issues arise from finite statistics and optical imperfections.
研究不足
The experimental setup has finite optical resolution at the SLM plane, leading to potential signaling in raw data due to overlap between spectral components, especially for qutrit measurements. The analysis assumes i.i.d. source and measurements, fair sampling, and negligible signaling effects, which may not hold perfectly. Finite sample size causes deviations from non-signaling conditions, and the method for finding nearest quantum correlations may have degeneracies.
1：Experimental Design and Method Selection:
The experiment involves preparing energy-time entangled photon pairs via spontaneous parametric down-conversion (SPDC) in a PPKTP crystal pumped by a laser. A pulse shaper with a spatial light modulator (SLM) is used for spectral manipulation. Sum-frequency generation (SFG) in another PPKTP crystal and single-photon counting modules (SPCM) are employed for detection. The methodology includes projecting continuous biphoton states onto discrete frequency-bin bases to realize entangled qubit and qutrit states, and performing optimized measurements to violate specific Bell inequalities.
2：Sample Selection and Data Sources:
Entangled photon pairs are generated from the SPDC process. The data consists of coincidence counts between idler and signal photons, measured over time to estimate joint conditional probabilities.
3：List of Experimental Equipment and Materials:
PPKTP crystal for SPDC and SFG, ND:YVO4 laser (Coherent Verdi V5, 532 nm), spatial light modulator (SLM, Jenoptik SLM-S640d), lenses (f=150 mm, 100 mm, 60 mm, 11 mm), prisms (P1-P4), beam dump, bandpass filter, single photon counting module (SPCM, ID Quantique id100-20-uln).
4：Experimental Procedures and Operational Workflow:
Pump laser light is focused into the PPKTP crystal to generate entangled photons. The photons pass through a pulse shaper with SLM for spectral modulation. After manipulation, photons are detected via SFG in a second crystal and SPCM. Coincidence counts are recorded for various measurement settings to compute probabilities.
5：Data Analysis Methods:
Data is analyzed using linear and semidefinite programming to compute quantum violations, visibilities, and entanglement measures like negativity. Statistical uncertainties are considered, and raw data is post-processed to approximate non-signaling quantum correlations.
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Laser
Verdi V5
Coherent
Pumps the PPKTP crystal to generate entangled photons via SPDC.
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Spatial Light Modulator
SLM-S640d
Jenoptik
Modulates the spectral phase and amplitude of entangled photons for projective measurements in frequency-bin bases.
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Single Photon Counting Module
id100-20-uln
ID Quantique
Detects up-converted photons after SFG for coincidence counting.
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PPKTP crystal
Used for spontaneous parametric down-conversion (SPDC) and sum-frequency generation (SFG) to generate and detect entangled photons.
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Lens
Focuses and images light in the experimental setup.
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Prism
Part of the pulse shaper for spectral dispersion and compression.
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Beam Dump
Absorbs residual pump light to prevent interference.
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Bandpass Filter
Filters out non-up-converted photons to improve signal-to-noise ratio.
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