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arXiv:2404.19304 · Physical Review A

Boosting the generation rate of squeezed single-photon states by generalized photon subtraction

Hiroko Tomoda, Akihiro Machinaga, Kan Takase, Jun Harada, Takahiro Kashiwazaki, Takeshi Umeki, Shigehito Miki, Fumihiro China, Masahiro Yabuno, Hirotaka Terai, Daichi Okuno, Shuntaro Takeda

Published Sep 23, 2024• 15 citations
arXivHTMLPDF

Abstract

In optical quantum information processing with continuous variables, optical non-Gaussian quantum states are essential for universal and fault-tolerant quantum computation. Experimentally, their most typical generation method is photon subtraction (PS), where single-photon detection by an on/off detector probabilistically heralds the generation of squeezed single-photon states. In PS, however, trying to avoid unwanted multiphoton detection inevitably limits the generation rate, hindering the application of squeezed single-photon states. Here, we theoretically show that generalized photon subtraction (GPS), a simple extension of PS, can improve the generation rate while maintaining the quality of the generated states. Furthermore, we experimentally demonstrate the generation rate improvement for 2-dB- and 4-dB-squeezed single-photon states compared to PS, by more than one order of magnitude, particularly for the case of 2 dB. Our results will accelerate the application of squeezed single-photon states to more advanced quantum information protocols.

DOI
10.1103/physreva.110.033717

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In optical quantum information processing with continuous variables, optical non-Gaussian quantum states are essential for universal and fault-tolerant quantum computation. Experimentally, their most typical generation method is photon subtraction (PS), where single-photon detection by an on/off detector probabilistically heralds the generation of squeezed single-photon states. In PS, however, trying to avoid unwanted multiphoton detection inevitably limits the generation rate, hindering the application of squeezed single-photon states. Here, we theoretically show that generalized photon subtraction (GPS), a simple extension of PS, can improve the generation rate while maintaining the quality of the generated states. Furthermore, we experimentally demonstrate the generation rate improvement for 2-dB- and 4-dB-squeezed single-photon states compared to PS, by more than one order of magnitude, particularly for the case of 2 dB. Our results will accelerate the application of squeezed single-photon states to more advanced quantum information protocols.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.
We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about 103{10}^{3}103 to 106{10}^{6}106 times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.
Wave--particle duality is a hallmark of quantum mechanics. For bosonic systems, there exists a continuum of intermediate states bridging wave-like Schrödinger cat states and particle-like Fock states. Such states have recently been recognized as valuable resources for enhancing fault-tolerant quantum computation (FTQC) with propagating light. Here we experimentally demonstrate tunable generation of these intermediate states by employing generalized photon subtraction (GPS). By detecting up to three photons from squeezed-light sources with a photon-number-resolving detector, we continuously control the balance between wave- and particle-like features. This approach allows us to construct a spectral family of quantum states with high generation rates, optimized according to the required fault-tolerance threshold. Our results establish GPS as a versatile toolbox for tailoring non-Gaussian resources, opening a pathway to efficient Gottesman--Kitaev--Preskill (GKP) qubit generation and addressing a central bottleneck in optical quantum computing.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
Schrödinger cat states are important non-Gaussian resources for quantum information processing and quantum-enhanced metrology. Although photon subtraction from squeezed vacuum states has proven useful for generating such states in the optical domain, scaling to large amplitudes while maintaining high fidelity and heralding probability remains challenging. To address these obstacles, we analyze alternating squeezing and photon-number-subtraction operations. Rather than optimizing for a single heralding outcome, we formulate cat-state generation as a fidelity-constrained multibranch problem, jointly optimizing the total probability of all photon-number outcomes satisfying a prescribed fidelity threshold at one common experimental setting. Already for plain photon subtraction, this provides a more operational measure of the usable generation probability and can favor parameter configurations that differ from single-branch optima. Considering experimental constraints on available squeezing and photon-number-resolving capability, we demonstrate improvements in fidelity and success probability compared with plain photon subtraction, without necessarily increasing the required squeezing resources. Without restrictions on photon-number resolution, we find that the optimal architecture of the alternating scheme reduces to one of two single-subtraction endpoint configurations, depending on the available squeezing resources. When photon-number resolution is additionally limited, genuinely alternating branches can become advantageous. We derive analytical expressions for the conditional states, cat-state fidelities, and heralding probabilities, enabling efficient multibranch optimization and a systematic analysis of resource trade-offs, sensitivity to experimental parameter deviations, and heralding loss. Together, these results identify the architecture best suited to a given resource budget.