Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference

arXiv:2502.06570 · quant-ph · Submitted 2025-02-10 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference".

Mira: The gist:

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, we're looking at this paper called "Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference." It tackles a real puzzle about parametric down-conversion sources and whether they produce entangled N00N states or just independent squeezers.

Mira: Exactly. The main point is that the way you describe the output really depends on whether you use a discrete or continuous variable approach, and this paper looks at how measuring things with photon number resolution helps sort out that difference.

Kai: It seems they take a hybrid approach, starting with the input state from parametric down-conversion and then checking out measurements using photon number resolved detection to see if the output is separable in the photon number picture.

Lev: So, what’s the core idea here for us as error correction folks? Are we talking about something that makes running real hardware easier or harder when you're dealing with these correlated states?

Mira: The paper starts by taking a phase space representation of an entangled TMSVS, and when you interfere that on a fifty:fifty beam splitter, you get two independent, phase shifted SMSVSs <ref:2502.06570#pg3,on a 50:50 beam splitter>.

Kai: Those SMSVSs are characterized by having squeezing in one direction and anti-squeezing in the other direction along orthogonal axes.

Lev: That sounds like a standard way to characterize squeezed light, but what’s the twist here with how they measure those correlations?

Mira: They introduce three different ways to measure correlation: a correlation coefficient, which is bounded between one and negative one and only sensitive to second-order correlation.

Kai: Then there’s the Schmidt decomposition, which gets into higher-order correlations, and mutual information which also looks at those higher orders.

Lev: So they are using these different tools to probe the state, but what did they actually find when they compared their simulation results with the experiment?

Mira: The experiment involved generating a TMSVS from a type-II PDC source in a periodically poled potassium titanyl phosphate waveguide and then interfering it on a balanced fiber beam splitter.

Kai: And they used photon number resolving detectors, which is pretty specific, to get those photon number statistics for the output ports.

Lev: What did they find out about those correlations when you looked at the temporal delays between the input pulses? That seems like where things get really interesting.

Mira: For temporal separations greater than negative four picoseconds, all three correlation measures showed correlations, which made sense given minimal interference. But at a zero picosecond delay, everything pointed toward near perfect interference.

Kai: And they found that for a zero picosecond delay, the Schmidt number was very close to one and the mutual information was consistent with zero within their measurement error bars.

Lev: That suggests that in that perfect interference case, the outputs are practically independent, which is exactly what you expect if you're dealing with two independent squeezers.

Mira: But they also noted that the correlation coefficient didn't go to zero at zero delay, and there was a difference between their experimental results and their simulation because of missing spectral multimodedness in the simulation.

Kai: So, to sum up what this paper on "Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference" is telling us about the hybrid approach they used, it’s that photon number statistics are separable in that picture.

Lev: It seems like the paper is really emphasizing the value of using photon number correlation measures for characterizing squeezed light sources when you're building things like Gaussian boson sampling.

Mira: They are showing that these correlation measures are a good way to characterize those sources for hybrid applications, even though we still have that initial debate about whether they are N00N states or just independent squeezers.

Kai: So, the main implication is that you can use these specific correlation measures to tell the difference between those two descriptions when you're actually measuring the output.

Lev: If we think about what this means for building quantum systems, it suggests that how we measure these states matters a lot for how well our error correction protocols work in practice.

Mira: Yeah, and it points toward using photon number correlations as a necessary tool when you're looking at the output of parametric down-conversion.

Kai: So, to wrap up on this paper, "Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference," it’s about showing how these interference experiments let us sort out the confusion between discrete and continuous variable descriptions.

Lev: It’s a practical look at how measurement choice affects the description of a quantum state generated by PDC.

Conclusion: Kai: So, we're wrapping up on "Erasing Photon-Number Correlations through Hong-Ou-Mandel Interference." This paper looks at how we can use interference experiments to sort out that confusion between discrete and continuous variable descriptions of light sources.

Mira: Right, so the big question here is what this means for describing these squeezed light states generated by parametric down-conversion. They're showing that when you look at the output ports, their photon number statistics actually separate cleanly in a specific picture.

Lev: If we think about running this on actual hardware, does this mean our error correction protocols become simpler or more complicated when dealing with these correlated states?

Kai: The authors are essentially saying that using photon number correlation measures gives us a way to characterize these sources, which is important for applications like Gaussian boson sampling. It moves the discussion from just looking at quadrature fluctuations to looking at actual photon counting.

Mira: They're making a point about the validity of different measurement tools by showing how they behave under specific conditions, like temporal delays. The results suggest that these correlation measures are quite useful for distinguishing between those two initial descriptions we talked about.

Lev: So for someone trying to build a real quantum system, does this mean we should be focusing our experimental design on measuring these photon number correlations instead of just the standard quadrature measurements?

Kai: It seems like the authors are strongly advocating for these photon-number correlation measures because they offer a more complete picture of the output state. It's about using those specific tools to really characterize what you're getting out of your setup.

Mira: The paper by Kai and Mira is important because it provides a concrete way to bridge that gap between theory and what we can actually measure in an experiment involving PDC sources. It’s showing how the measurement choice dictates the description of the quantum state itself.

Lev: And if this approach works, what does that imply for future work in quantum optics experiments? Does this open up new possibilities for characterizing different types of non-classical light?

Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Paderborn, Germany · Department of Applied Physics, School of Engineering, The University of Tokyo, Tokyo, Japan · School of Physics and Astronomy, University of Glasgow, Glasgow G4 8QQ, UK

quant-ph

Submitted: 2025-02-10

Updated: 2026-10-09

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: The gist: The study experimentally verifies for the first time that photon number statistics generated by HOMI of a TMSVS are in fact decorrelated by measuring the statistics of the two output modes

Key concepts

Parametric Down-Conversion Source (PDC): This is a source that generates entangled pairs of photons by splitting a high-energy pump beam into two lower-energy photons. In this specific experiment, it was generated using a type-II PDC source in a periodically poled potassium titanyl phosphate waveguide, producing nearly single spectral mode pulses.
Hong-Ou-Mandel Interference (HOMI): HOMI is an interference phenomenon where two identical photons entering a beam splitter exhibit specific correlations. The experiment used HOMI to interfere the generated photon pairs, which allowed researchers to probe the statistical properties of the resulting output modes.
Photon Number Correlation Measures: These are mathematical tools—including correlation coefficients, Schmidt decomposition, and mutual information—used to quantify how correlated or independent two quantum systems are. The paper shows these measures reveal that the output states from this specific interference setup are separable in the photon number picture.
Continuous-Variable (CV) vs. Discrete-Variable (DV) Approaches: This refers to two different mathematical frameworks used to describe quantum light, where one treats light as a continuous wave and the other as discrete photons. The study investigates how taking these different approaches leads to distinct predictions about the output statistics of squeezed light sources.

Terminology

Hybrid Approach — 1× in this paper · explained in 4 episodes

Summary

The gist: The study experimentally verifies for the first time that photon number statistics generated by HOMI of a TMSVS are in fact decorrelated by measuring the statistics of the two output modes up to eight clicks, demonstrating that CVQO and DVQO descriptions yield different results due to conditioning on at least one photon.

Concept and Theory

The work investigates the disparity between describing parametric down-conversion (PDC) light as a source of entangled N00N-states or independent, uncorrelated squeezers based on whether a standard discrete- or continuous-variable approach is taken <ref:2502.06570#pg2>. The authors take a hybrid approach to describe the state, investigating measurements using photon number resolved detection and showing that the output of this interference is separable in the photon number picture <ref:2502.06570#pg2>.

The concept involves starting with a phase space representation of a quadrature entangled TMSVS <ref:2502.06570#pg4>. Interfering this TMSVS on a 50:50 beam splitter results in two independent, phase shifted, SMSVSs <ref:2502.06570#pg4>. These SMSVSs are characterized by exhibiting quadrature fluctuations below the vacuum level along one axis (squeezing) and fluctuations higher than the vacuum level along the orthogonal axis (antisqueezing) <ref:2502.06570#pg4>.

The authors introduce three methods to measure correlation:

The correlation coefficient, defined as corr(PC, PD) = cov(PC, PD) / (σPC σPD), which is bounded between 1 and-1 <ref:2502.06570#pg4>. This measure is sensitive only to the degree of second-order correlation <ref:2502.06570#pg4>.
The Schmidt decomposition, which is sensitive to higher-order correlations <ref:2502.06570#pg5>. For a TMSVS, this decomposition yields a Schmidt number K = 1/P∞ i=0 λi2 <ref:2502.06570#pg5>.
The mutual information I(PC, PD), defined as I(PC, PD) = Σ nc,nd P(nc, nd) log10 P(nc, nd)/P(nc)P(nd) <ref:2502.06570#pg5>. This measure is sensitive to higher-order correlations <ref:2502.06570#pg5>.

Experiment

The TMSVS was generated with a type-II PDC source in a periodically poled potassium titanyl phosphate waveguide <ref:2502.06570#pg4>. The source generates nearly a single spectral mode, pulsed, spectrally degenerate TMSVS with an effective number of spectral-modes of 1.3 <ref:2502.06570#pg5>. High interference visibility was achieved in a HOMI experiment at 94% <ref:2502.06570#pg5>.

The experimental setup involved splitting the generated photon pairs on a polarizing beam splitter (PBS) and interfering them at a balanced fiber beam splitter (BS) with an adjustable delay <ref:2502.06570#pg4>. Photon number resolved detection (PNR) was achieved via two independent 8 time-bin time-multiplexed detectors (TMDs) <ref:2502.06570#pg5>. The mean photon number was measured at 0.060 ± 0.008 in the high efficiency arm.

Results

The joint click statistics were converted to pseudo-photon number correlations using a method from [35]. The results showed that all three correlation measures followed their respective simulations rather closely, testifying to the high single mode quality of the source.

Key findings regarding temporal delays include:

**- For temporal separations greater than −4 ps, all three correlation measures show correlations, consistent with minimal interference. The correlation coefficient is noted as being more sensitive to the effects of multimodedness than the other two measures. 3) The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0. The main difference between the experiment and simulation is the missing spectral multimodedness in the simulation. In contrast, for a temporal delay of 0 ps, the value of the Schmidt number is very close to 1 and the mutual information is consistent with 0 inside the error margin, due to near perfect interference. This indicates that the outputs are very close to independent, as one would expect in the ideal case of two independent squeezers. The correlation coefficient shows a similar shape as the other two measures but does not go to 0.

Improvements for AI systems

The AI system can be trained to accurately characterize squeezed light sources for hybrid applications like Gaussian boson-sampling by utilizing photon-number correlation measures, as shown in we demonstrate the worth of photon-number correlation measures for the characterization of squeezed light sources for hybrid applications like Gaussian boson-sampling.
The system can perform high-fidelity quantum state verification by comparing experimental joint click statistics with simulations that incorporate experimental losses and matched to the experimental settings, allowing it to assess the quality of single spectral mode sources based on good agreement between experiment and simulation is testimony to the high single mode quality of our source.
The AI can develop new metrology capabilities by applying measurements to produce Holland-Burnett states, which are described as states that approximate the interferometric qualities of N00N-states, but are almost optimally resilient to experimental imperfections.
The system can be adapted for advanced quantum information processing by utilizing the knowledge that the conditioning of the photon counting measurements on having at least one photon, effectively removing the vacuum component P(0, 0) from the joint probability distribution introduces correlated information about the two-mode state, which leads to the creation of an entangled N00N-state.
The system can gain superior discrimination capabilities in quantum optics by using the correlation coefficient, noting that it is more sensitive to multimodedness than the other two measures and can be used as a better measure for finding the best temporal overlap in the measured joint photon number distributions.

Abstract

A parametric down-conversion source interfering on a beam splitter can be described as both a source of entangled N00N-states or a source of independent, and thus uncorrelated squeezers. The disparity between these outcomes can be attributed to whether one takes a standard discrete- or continuous-variable approach to describing the system. More precisely, this difference in output is due to the types of measurements involved and the way in which the data is processed, as both setups are identical, clearly identical states are produced. Here we take a hybrid approach to describe the state, which is generated by parametric down-conversion as input state, and investigate the measurements of the output ports of the interferometer using photon number resolved detection. We show that the output of this interference is separable in the photon number picture and demonstrate the worth of photon-number correlation measures for the characterization of squeezed light sources for hybrid applications like Gaussian boson-sampling.