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Journal of the Optical Society of America B

Enlarging the Schrödinger cat state through the superposition of two kitten states in coupled waveguides

Nuo Wang, Xinchen Zhang, Qi Liu, Feng-Xiao Sun, Qiongyi He, Ying Gu

Published Mar 3, 2025• 0 citations
Publisher

Abstract

The optical Schrödinger’s cat is highly anticipated for its potential to realize fault-tolerant quantum computing and quantum metrology. To attain a good performance in these processes, the amplitude of cat states is desired to be as high as possible. Here, we demonstrate the enlargement of a cat state through the superposition of two kitten states in coupled waveguides. Under reasonable superposition coefficients, the interference between two nearby coherent state components in the initial kittens will produce a coherent-like state with a larger amplitude, enabling the creation of larger cat-like states. Based on the above mechanism, we theoretically demonstrate the superposition of two kittens in coupled waveguides through conditional measurements. In an appropriate propagation length, a cat state, whose amplitude is enlarged beyond α 0 2 + β 0 2 , is achieved with high fidelity and a high success probability when the amplitudes of input kittens are α 0 and i β 0 , respectively. The mechanism we propose has the potential to be realized in other systems, and it could be extended to amplify other macroscopic quantum states. The physical realization based on coupled waveguides demonstrates the ability to efficiently amplify cat states and is expected to become a competitive approach for on-chip cat state preparation.

DOI
10.1364/josab.554233

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The optical Schrödinger’s cat is highly anticipated for its potential to realize fault-tolerant quantum computing and quantum metrology. To attain a good performance in these processes, the amplitude of cat states is desired to be as high as possible. Here, we demonstrate the enlargement of a cat state through the superposition of two kitten states in coupled waveguides. Under reasonable superposition coefficients, the interference between two nearby coherent state components in the initial kittens will produce a coherent-like state with a larger amplitude, enabling the creation of larger cat-like states. Based on the above mechanism, we theoretically demonstrate the superposition of two kittens in coupled waveguides through conditional measurements. In an appropriate propagation length, a cat state, whose amplitude is enlarged beyond α 0 2 + β 0 2 , is achieved with high fidelity and a high success probability when the amplitudes of input kittens are α 0 and i β 0 , respectively. The mechanism we propose has the potential to be realized in other systems, and it could be extended to amplify other macroscopic quantum states. The physical realization based on coupled waveguides demonstrates the ability to efficiently amplify cat states and is expected to become a competitive approach for on-chip cat state preparation.
Optical Schrodinger's cat (SC) is highly anticipated because of the potential of realizing fault-tolerant quantum computing, but the practical merit is only shown when the amplitude is larger than 2. However, such high-amplitude cats have not been prepared due to the limitations rooted in the existing method. Here, we demonstrate a principle that a large SC-like state can be generated by the superposition of two kittens in which two nearby coherent states interfere and grow to an enlarged coherent-like state. Further, we propose a scheme to breed the cat beyond the limitation in the former works with a high probability by realizing the superposition of two SCs in coupled waveguides. The principle and scheme demonstrated here provide a new perspective on understanding quantum superposition in phase space and a better solution for the efficient generation of SCs on chips.
We demonstrate an optical method to engineer optical Schrödinger cat states (SCSs) of large size beta ranging from beta=2 to beta=3 with high fidelity close to 0.99. Our approach uses the alpha-representation of the SCSs in infinite Hilbert space with base in terms of displaced number states characterized by the displacement amplitude alpha. An arbitrary alpha-representation of SCSs enables manipulation of the amplitudes in wider ranges of parameters, greatly expanding the possibilities for generation of desired nonclassical states. The optical scheme we consider is quite universal for implementation of the conditioned states close to SCSs with use of linear-optics elements and detectors projecting unitarily transformed input states onto the target one. Different states (e.g., number state or coherent state or superposed state) are selected as the input to the optical scheme. In particular, an input small-size Schroodinger kitten state can give rise to an output large-size SCS.
Superpositions of macroscopically distinct quantum states, introduced in Schrödinger’s famous Gedankenexperiment, are an epitome of quantum “strangeness” and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger’s cat — the superposition of two opposite-amplitude coherent states — is also the backbone of quantum information processing in the continuous-variable domain. Here we implement two protocols for producing and amplifying optical Schrödinger’s cats. In the first protocol we remotely prepare a high-efficiency Schrödinger cat state by applying the remote state preparation to a N00N state prepared between two parties that are separated by a lossy medium. The second protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. The latter technique enables implementation in an iterative manner, in principle allowing creation of Schrödinger’s cat states of arbitrarily high amplitude.
Abstract Generation of the states with fidelity as close as possible to high-amplitude Schrödinger cat states (SCSs) is studied. The input state in the main mode is exclusively mixed with the Fock states on successive beam splitters after which a number of auxiliary modes emerge. Subsequently, all the modes are properly displaced. The resulting state is projected onto the vacuum states of every auxiliary mode for conditional generation of the target states in the main mode. We demonstrate a possibility to generate Schrödinger cat qudits (SCQs) which may approximate SCSs of large size β ranging from β = 2 to β = 3 with high fidelity close to 0.99 . The method is based on the use of the concept of SCQs being the best approximation of the SCSs in the finite Hilbert space with basic displaced number states characterized by the displacement amplitude α . Different states (e.g. number state or coherent state or superposed state) are selected as the input to the optical scheme. In particular, we show that an input Schrödinger kitten state (i.e. small-size SCS) can give rise to an output SCS of larger size. We also test the proposed approach in a realistic scenario.
We present novel theory of effective realization of large-size optical Schrödinger cat states, which play an important role for quantum communication and quantum computation in the optical domain using laser sources. The treatment is based on the α-representation in infinite Hilbert space which is the decomposition of an arbitrary quantum state in terms of displaced number states characterized by the displacement amplitude α. We find analytical form of the α-representation for both even and odd Schrödinger cat states which is essential for their generation schemes. Two schemes are proposed for generating even/odd Schrödinger cat states of large size |β| (|β| ≥ 2) with high fidelity F (F ≈ 0.99). One scheme relies on an initially offline prepared two-mode entangled state with a fixed total photon number, while the other scheme uses separable photon Fock states as the input. In both schemes, generation of the desired states is heralded by the corresponding measurement outcomes. Conditions for obtaining states useful for quantum information processing are established and success probabilities for their generation are evaluated.
We proposed and analyzed a scheme to generate large-size Schr\"odinger cat states based on linear operations of Fock states, squeezed vacuum states, and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced small-amplitude Schr\"odinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schr\"odinger odd kitten states with amplitudes of $|\ensuremath{\beta}|=1.06$ and $|\ensuremath{\beta}|=1.11$ generated from one-photon-subtracted 3 dB squeezed vacuum states, are amplified to an odd cat state of $|\ensuremath{\beta}|=1.73$ with a fidelity of F=99F=99%F=99. A large-size Schr\"odinger odd cat state with $|\ensuremath{\beta}|=2.51$ and F=97.30F=97.30%F=97.30 is predicted when 5.91 dB squeezed vacuum states are employed. According to the analysis on the impacts of experimental imperfections in practice, Schr\"odinger odd cat states of $|\ensuremath{\beta}|>2$ are available. A feasible configuration based on a quantum frequency comb is developed to realize the large-size cat state generation scheme we proposed.