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arXiv:2412.14798 · Physical Review Applied

Efficient generation of optical cat states using squeezed few-photon superposition states

Haoyuan Luo, Sahand Mahmoodian

Published Jan 8, 2026• 3 citations
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Abstract

Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Yet the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here, we propose using squeezed superpositions of zero and two photons, $|θ\rangle = \cos{(θ/2)}|0\rangle + \sin{(θ/2)}|2\rangle$, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability $P\gtrsim 50\%$ that can generate cat states of size $|α|^2=5$ with fidelity $F>0.99$. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with $2\%$ detection loss still achieving $F>0.98$ for cats with $|α|^2=5$. We also show that squeezed $θ$ states are ideal candidates for nonlinear photon subtraction using a two-level system with near deterministic success probability and fidelity $F>0.98$ for cat states of size $|α|^2=5$. Schemes for generating $θ$ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.

DOI
10.1103/t96h-488y

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We report an efficient way to generate both even and odd optical analogs of Schrodinger cat states (SCSs) which are a superposition of two coherent states with opposite amplitudes. The resources consumed are single mode squeezed vacuum (SMSV) state and single photon. SCSs are formed after superimposing the input states with the subsequent detection of the number of photons in the auxiliary mode. We report the generation of even/odd SCSs with amplitude 4.2 with fidelity >0.99 and an acceptable for offline experiments success probability. There is a tendency towards an increase in the size of the SCSs with the fidelity >0.99 more demonstrated with an increase in the number of extracted photons.
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.
The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.
Abstract We theoretically propose an efficient way to generate optical analogs of both even and odd Schrӧdinger cat states (SCSs) of large amplitude with high fidelity and reasonable generation rate. The resources consumed are a single-mode squeezed vacuum state (SMSV) and possibly a single photon or nothing. We report the generation of even (odd) SCS with amplitude 4.2 , fidelity higher than 0.99 with success probability a little more than 10 − 7 by subtraction of 30 ( 31 ) photons from SMSV by ideal photon number detection. In order to reduce the requirements for the sensitivity of photon number resolving (PNR) detector, we show the implementation of even/odd SCSs with the same characteristics with two PNR detectors resolving only 15 photons each instead of 30 . In the case of inefficient detector, SCS’s size and its fidelity can be kept close to perfect by using highly transmitting beam splitter, but at the cost of very dramatic reduction of the success probability. In order to have certain harmony between the characteristics (large amplitude, high fidelity and acceptable success probability) in the case of imperfect detection, highly transmitting beam splitters should not be used and number of the subtracted photons must be reduced to 10 11 .
Optical "Schrödinger cat" states, the non-classical superposition of two quasi-classical coherent states, serve as a basis for gedanken experiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical "Schrödinger cats" by adding a photon to a squeezed vacuum state, so far only photon-subtraction protocols have been realized. Photon-addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate "Schrödinger cats" at rates exceeding 8.5×1048.5 \times 10^48.5×104 counts per second; at least one order of magnitude higher than all previously reported realizations. Wigner distributions with pronounced negative parts are demonstrated at down to -8.89 dB squeezing, even when the initial squeezed vacuum input state has low purity. Benchmarking against such a degraded squeezed input state we report a maximum fidelity of more than 80% with a maximum cat amplitude of ∣α∣≈1.66|α| \approx 1.66∣α∣≈1.66. Our experiment uses photon-addition from pairs, one of those photons is used for monitoring, giving us enhanced control; moreover the pair production rates are high and should allow for repeated application of photon-addition via repeat-stages.