⚛️ quantum physics

Compound beams for direct experimental comparison of quantum operations

This paper proposes a compound beam approach to experimentally compare quantum operations, demonstrating that photon addition generally enhances nonclassicality in thermal and sub-Poissonian beams while photon subtraction is superior for twin beams, with optimal conditions identified for generating highly nonclassical states.

Original authors: Kishore Thapliyal, Jan Perina Jr., Pavel Pavlicek, Antonin Cernoch

Published 2026-08-11

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CC BY 4.0

Original authors: Kishore Thapliyal, Jan Perina Jr., Pavel Pavlicek, Antonin Cernoch

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where light isn't just a wave or a stream of particles, but a toolbox for building the future. This is the realm of quantum physics, specifically the "second quantum revolution," where scientists are learning to harness the weird, counter-intuitive rules of the very small to build super-fast computers, unbreakable codes, and sensors that can see the invisible. To do this, they need special kinds of light called "nonclassical states." Think of normal light (like from a lamp) as a calm, predictable crowd. Nonclassical light is more like a tightly choreographed dance troupe where every move is perfectly synchronized, or a crowd that suddenly decides to move in perfect silence. These special states are the fuel for quantum technologies, but they are notoriously difficult to create and control.

To get this special light, scientists often start with a "twin beam"—a pair of light streams born from the same source, like identical twins who share a secret language. They then try to tweak these beams using two main tricks: "photon addition" (adding a tiny bit of extra light energy) and "photon subtraction" (snipping away a tiny bit). The big question has always been: which trick works better? Does adding light make the dance more synchronized, or does cutting it away work better? Until now, comparing these tricks fairly has been like trying to compare the speed of a Ferrari and a bicycle by testing them on different tracks with different weather. The conditions were never the same, making it hard to know which tool was truly superior for the job.

This paper steps in to settle the score by building a "compound beam" laboratory. The researchers created a clever setup where they could take the exact same source of light and apply both the "add" and "subtract" tricks side-by-side, like a fair fight in a boxing ring. They tested these operations on three different types of light: "thermal" light (like the chaotic glow of a lightbulb), "sub-Poissonian" light (a very orderly, quiet stream), and "twin beams" (the synchronized pairs). They added or subtracted up to twenty tiny packets of light (photons) at a time to see how the light's personality changed.

The results were a mix of surprises and clear winners. When they worked with the chaotic thermal light or the orderly sub-Poissonian light, "photon addition" was the champion. Adding photons made these beams much more "nonclassical," turning them into the high-performance fuel needed for quantum tasks. However, when they turned to the synchronized "twin beams," the rules flipped. Here, "photon subtraction" was the star player, outperforming addition by creating stronger quantum effects. The paper also discovered that by using a special timing trick with the twin beams, they could simulate an "ideal" addition of photons, getting even closer to the perfect quantum states scientists dream of. While the paper doesn't claim to have built a quantum computer yet, it provides a clear map for engineers, showing exactly which tool to grab depending on the type of light they are working with, helping to optimize the next generation of quantum devices.

Technical Summary: Compound Beams for Direct Experimental Comparison of Quantum Operations

Problem Statement
The generation of highly nonclassical and entangled multi-mode states is essential for quantum communication, metrology, and information protocols. While photon addition (PA) and photon subtraction (PS) are established non-Gaussian operations used to induce or enhance nonclassicality, a direct, fair experimental comparison of their effectiveness across different quantum states has been lacking. Previous studies often utilized different light sources or parameters for different operations, making mutual comparisons difficult. Furthermore, while theoretical advantages of PA and PS are well-documented, their experimental suitability under comparable conditions remains an open question, particularly for multi-mode fields where bosonic commutation relations are less dominant but statistical properties are complex.

Methodology
To overcome the obstacle of comparing operations on disparate sources, the authors employ "compound beams." These are constructed by concatenating temporal detection windows of weak twin beams (TWBs) generated via spontaneous parametric down-conversion (SPDC) in a LiIO3 crystal. This temporal multiplexing approach allows the creation of compound beams with intensities varying over two orders of magnitude while maintaining a common experimental origin.

The study focuses on three fundamental types of optical fields derived from the same source:

Twin Beams (TWB): Entangled signal-idler pairs.
Thermal States (TS): The marginal signal beam of the TWB.
Sub-Poissonian States (SPS): The signal beam conditioned on specific photon-number detection in the idler beam.

The authors experimentally apply PA and PS to these three base states, creating nine distinct groups of states (e.g., Photon-Added Twin Beam, Photon-Subtracted Thermal State, etc.).

Photon Addition (PA): Implemented by post-selecting an auxiliary TWB based on idler photocounts and adding its signal component to the primary beam.
Photon Subtraction (PS): Simulated by effectively splitting the detection windows of the primary signal beam, where a subset of windows mimics the reflected arm of a beam splitter, conditioned on detecting specific photocounts in the "reflected" portion.

The experimental setup utilizes synchronized avalanche photodiodes (APDs) to record signal and idler photocounts. Data processing involves constructing 1D and 2D photocount histograms, which are then inverted using a maximum-likelihood reconstruction method to retrieve photon-number distributions. The nonclassicality of the resulting states is quantified using the Fano factor ( $F$ ) and the noise-reduction parameter ( $R$ ), as well as the nonclassicality depth ( $\tau$ ).

Key Results
The study provides a quantitative comparison of PA and PS across the three field types:

Twin Beams (TWB): Photon subtraction outperforms photon addition in inducing nonclassicality in the marginal signal beam. However, this comes at the cost of significantly disturbing the quantum correlations (entanglement) between the signal and idler beams, as evidenced by a degradation in the noise-reduction parameter $R$ .
Thermal States (TS) and Sub-Poissonian States (SPS): In contrast to TWBs, photon addition is identified as advantageous over photon subtraction. PA successfully induces (in TS) or enhances (in SPS) nonclassicality, whereas PS fails to generate a nonclassical state in TSs and offers limited enhancement in SPSs.
Intensity Dependence: The effects of PA and PS are negligible when the number of added or subtracted photons is small compared to the mean photon number of the beam. Significant changes occur only when the number of manipulated photons is comparable to the mean photon-pair number.
Ideal vs. Real Operations: By exploiting temporal photon-pair correlations, the authors demonstrate "ideal" photon addition (mimicking a photon-number-resolving detector). Ideal PA yields greater nonclassicality than standard PA, particularly in SPSs, where it significantly increases the beam's nonclassicality depth.

Significance and Claims
The paper claims that the compound beam technique provides a versatile platform for the direct, fair experimental comparison of quantum operations that was previously unattainable due to source incompatibility. The authors demonstrate that the choice between PA and PS is not universal but depends critically on the underlying quantum state:

PA is superior for thermal and sub-Poissonian states.
PS is superior for twin beams regarding nonclassicality generation, though it degrades entanglement.

The study highlights that compound beams can simulate ideal detection schemes and analyze beams with intensities differing by orders of magnitude within a single setup. The authors conclude that these structures can be directly embedded into more complex quantum information protocols, offering potential for optimizing nonclassical light sources and implementing quantum communication and metrology schemes. The work establishes a foundational experimental framework for selecting the optimal non-Gaussian operation for specific quantum applications.

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