研究目的
To experimentally test the recently derived duality relation between quantum coherence and path information using l1-norm measure and minimum-error state discrimination.
研究成果
The experimental results confirm Bagan's equality, showing a trade-off between quantum coherence and path information. This validates the new duality relation and highlights the role of coherence in quantum mechanics, with implications for quantum technologies and fundamental research.
研究不足
The experiment is limited to N=2 paths, and the entanglement quality, though high, introduces small deviations in results. The use of postselection for state retrieval may not cover the full system state, and technical challenges remain for extending to multi-path scenarios.
1：Experimental Design and Method Selection:
The experiment uses a Sagnac interferometer to generate polarisation-entangled photon pairs via type-II spontaneous parametric down-conversion. Quantum state tomography is employed to reconstruct states, and l1-norm coherence and minimum-error state discrimination are used to quantify wave and particle behaviors.
2：Sample Selection and Data Sources:
Two-photon states are prepared with different levels of entanglement by inserting Brewster windows or a polarisation beam splitter to introduce polarisation-dependent loss. Three classes of states are generated with varying parameters.
3：List of Experimental Equipment and Materials:
A 405 nm UV laser, single-mode fiber, half-wave plates, quarter-wave plates, polarisation beam splitter, periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal, bandpass filters, fused silica Brewster windows, and single-photon counting modules.
4：Experimental Procedures and Operational Workflow:
Photon pairs are generated, their polarisation is manipulated with waveplates and Brewster windows, states are analyzed using tomography with HWP, QWP, and PBS, and coincidences are detected. Data is collected for different state preparations.
5：Data Analysis Methods:
Coherence (C) is calculated from density matrices, path information (P) is derived from success probabilities in state discrimination, and Monte Carlo simulations with Poissonian statistics are used for error analysis.
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UV laser
405 nm
Pumps the PPKTP crystal to generate photon pairs via spontaneous parametric down-conversion.
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Half-wave plate
Adjusts the polarisation of the laser and photons.
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Quarter-wave plate
Adjusts the polarisation of the laser and photons.
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Polarisation beam splitter
Splits and combines light based on polarisation in the Sagnac interferometer and state analysis.
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PPKTP crystal
25 mm long
Generates entangled photon pairs via type-II spontaneous parametric down-conversion.
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Bandpass filter
3 nm
Filters the down-converted photons to select the desired wavelength.
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Fused silica Brewster window
Introduces polarisation-dependent loss to generate non-orthogonal detector states.
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Single-photon counting module
Detects single photons for coincidence measurements.
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Single-mode fiber
Guides the laser and photon beams to ensure spatial mode quality.
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