Compound beams for direct experimental comparison of quantum operations

AI summary

Overview

Research area: Experimental quantum optics — non-Gaussian quantum operations (photon addition and photon subtraction) applied to multi-mode nonclassical light, and a technique called "compound beams" that allows these operations to be compared under identical conditions.

Technical level: Intermediate. The paper uses photon-number statistics (Fano factor, noise-reduction parameter, nonclassicality depth) and reconstructs photon-number distributions from avalanche-photodiode data, but the core ideas are stated without heavy formalism.

Scope (one sentence): The paper uses compound beams built from synchronized detection windows of a weak twin beam to experimentally compare multi-photon addition and subtraction (up to 20 photocounts) applied to twin beams, thermal states, and sub-Poissonian states with intensities spanning two orders of magnitude.

What This Paper Is About

Photon addition and photon subtraction are standard non-Gaussian operations used to create or enhance nonclassical, entangled states, but they are usually tested on different light sources with different parameters, so their performance cannot be fairly compared. The authors solve this by deriving all three source types — twin beams, thermal states, and sub-Poissonian states — from a single parametric down-conversion source and packaging the raw photocounts into "compound beams" whose structure can be reshaped to emulate both operations. The goal is to identify, on equal experimental footing, which operation produces more nonclassical states and under what conditions.

Key Contributions

1. A single-source comparison platform. The authors construct all nine state groups (TWB, PATWB, PSTWB, TS, PATS, PSTS, SPS, PASPS, PSSPS) from the same LiIO₃ down-conversion source, so photon addition and subtraction are compared with identical detectors, losses, and noise.

2. Experimental multi-photon addition and subtraction up to 20 photocounts. Photon subtraction is emulated by grouping detection windows to mimic a beam splitter with transmissivity T_s = 1 − M̄_s/M_w, and photon addition by post-selecting an auxiliary twin beam conditioned on 1, 5, or 20 idler photocounts.

3. Systematic ranking of the two operations per state type. The paper establishes that addition wins for thermal and sub-Poissonian states while subtraction wins for twin beams, with the caveat that subtraction disturbs quantum correlations more.

4. A demonstration of near-ideal photon addition. Exploiting temporal photon-pair correlations in compound twin beams under post-selection, the authors implement what they call ideal photon addition, with generation probabilities of 8.10%, 1.05%, and 0.18% (relative error 1%) for 1, 2, and 3 ideally added photons.

Main Findings

• Photon addition induces nonclassicality in thermal states. Adding photons to a multi-mode thermal state raises the mean photon number and drives the Fano factor below one; the more photons added, the stronger and more nonclassical the beam. Photon subtraction lowers the intensity and reduces the Fano factor but does not produce a nonclassical state.

• Neither operation much improves sub-Poissonian states in the real (non-ideal) case. Addition increases and subtraction decreases the mean signal photon number, but the nonclassicality already present in the sub-Poissonian state is not significantly enhanced.

• Subtraction outperforms addition in twin beams. Comparing the Fano factor of the photon-added signal beam with that of the photon-subtracted idler beam shows smaller values for subtraction; the authors attribute this to the smaller mean photon numbers in the subtracted idler beam. The price is that subtraction disturbs the inter-beam quantum correlations (quantified by the noise-reduction parameter R) more strongly.

• Effects vanish when the beam is bright relative to the operation. Once the number of added or subtracted photons is considerably smaller than the mean photon or photon-pair number, both operations modify the original beam only negligibly. Conversely, larger photon numbers produce stronger changes, more nonclassical marginal beams, and weaker remaining quantum correlations.

• Success probabilities are high and match theory. For 1, 5, and 20 added photons the measured success probabilities are 38.99%, 18.60%, and 9.40% (theory: 38.03%, 18.15%, 9.16%); for 1, 5, and 20 subtracted photons they are 38.98%, 18.59%, and 9.40% (theory: 38.50%, 18.30%, 9.20%), with relative error 1%.

• Ideal addition reveals the true potential of the operation. Ideal photon addition produces greater nonclassicality than realistic addition in both thermal and sub-Poissonian states, and unlike realistic addition it can considerably increase the nonclassicality of sub-Poissonian states.

• Simple witnesses track the full nonclassicality depth. The quantities 1 − F and 1 − R follow the same dependence on concatenated-window number and added-photon number as the corresponding nonclassicality depths τ, and the actual depth τ_P exceeds 0.5 for low-intensity photon-added twin beams, certifying their non-Gaussian character (the Gaussian border is τ = 0.5).

Methodology in Plain English

The experiment uses type-I parametric down-conversion in a LiIO₃ crystal pumped by the third harmonic of an Nd-YAG laser at 355 nm with a 2.5 kHz repetition rate, producing weak twin beams at degenerate wavelengths centered at 710 nm. The pump is spectrally cleaned with dichroic mirrors and a 10-nm-wide filter and spatially filtered by a 4f system of two lenses (20 mm and 50 mm focal lengths) with a 50-μm round aperture. Signal and idler photons are coupled into multi-mode fibers through lenses of 15.3 mm focal length and detected by two avalanche photodiodes (Count-NIR, nominal efficiency about 80%, dark counts below 50 Hz). Pump pulses are 6.5 ns long with 4 ms between pulses, and the laser power is feedback-stabilized, with adjustment whenever the detection rate drifted by more than 5%.

The beams are so weak that each 6.5 ns detection window contains either zero or one photocount. The trick is to concatenate neighboring windows: joining up to 200 windows yields compound twin beams with up to roughly 80 mean photon pairs, and the full dataset of M_m = 645 × 10⁶ simple measurements supplies large ensembles. Every second entry is swapped between the signal and idler channels to symmetrize the two detection paths. Marginal histograms give thermal states, and histograms conditioned on a fixed idler count give sub-Poissonian states.

Photon subtraction is simulated by splitting the M_w signal windows into M_w − M̄_s and M̄_s parts, mimicking a beam splitter of transmissivity T_s = 1 − M̄_s/M_w, with M̄_s = 4, 22, and 90 windows used to subtract 1, 5, and 20 photocounts. Photon addition draws an auxiliary twin beam from M̄_a = 4, 22, and 90 windows and post-selects on 1, 5, or 20 idler counts. Photocount histograms are converted to photon-number distributions by inverting the detection matrix (efficiency η = 0.266 ± 0.005, dark count rate d = 6.6 × 10⁻³) with a maximum-likelihood method, and the twin-beam statistics are modeled as a convolution of Mandel-Rice distributions with parameters B_p = 0.159, M_p = 5M_w/2 for the pair component and B_s = 0.003, M_s = 5M_w/2 for the noise components, reflecting five independent modes per beam component per symmetrized double window.

Why This Matters

Impact on research. The work gives the first like-for-like experimental benchmark of photon addition versus photon subtraction across three canonical state families, removing the confound of comparing different sources. It also shows that compound beams can emulate an ideal photon-number-resolving detector, which lets experimenters estimate the ceiling of what an operation could achieve before committing to hardware.

Real-world applications

• Quantum key distribution and quantum communication, which rely on nonclassical and entangled multi-mode states.
• Quantum metrology and sensing, where non-Gaussian states improve sensitivity.
• Quantum imaging, including protocols that exploit photon-pair correlations.
• Quantum error correction with cat codes and GKP codes, which require photon subtraction to build coherent-state superpositions, and entanglement distillation.

Industry relevance. The results give photonic quantum technology developers a practical rule for choosing between addition and subtraction given a source type and brightness, and the compound-beam method works with standard avalanche photodiodes rather than demanding photon-number-resolving hardware, which lowers the barrier for benchmarking quantum light sources and detectors.

Future Directions

• Mapping temporal to spatial multiplexing. The authors note a one-to-one mapping between the temporal multiplexing used here and spatially resolved detection with intensified CCD cameras or matrix single-photon-sensitive detectors, where the compound beams would exist as real fields in an actual setup.

• Embedding full protocols in the compound-beam structure. The paper states that the building-block structure can be generalized to incorporate operations implementing complete quantum information protocols, not just state preparation.

• Pushing ideal photon addition further. Since ideal addition reveals the operation's true potential, a natural next step is extending it to larger added-photon numbers and testing whether it opens new routes for quantum technologies.

• Limits of the approach. The technique is designed for intensity properties and is explicitly not suitable for addressing field phase properties, so extending compound beams to phase-sensitive measurements remains open; likewise, results are restricted to beams with mean photon number per mode much less than one.

Target Audience

Experimental quantum opticians and photonics researchers working with parametric down-conversion sources, non-Gaussian state engineering, or photon-number-resolved detection; graduate students entering quantum optics who need a concrete worked example of state reconstruction and nonclassicality quantification; and quantum technology developers looking for an experimentally grounded guide to choosing between photon addition and photon subtraction for a given source.

Authors’ abstract

Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated. The results apply for the beams with mean photon number per mode much less than one.