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arXiv:2508.14750 · Physical Review A

Efficient nonclassical state preparation via generalized parity measurement

Chen-yi Zhang, Jun Jing

Published Jan 28, 2026• 1 citation
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Abstract

Nonclassical states of bosonic modes, especially the large number states, are valuable resources for quantum information processing and quantum metrology. It is however intricate to generate a desired Fock state of bosonic systems by unitary protocols due to their uniform energy spectrum. We here propose a nonunitary protocol that is based on the resonant Jaynes-Cummings interaction of the bosonic mode with an ancillary two-level atom and sequential projective measurements on the atom. Using the generalized parity-measurement operator constructed by several rounds of free evolution with stepwise halved intervals and measurement, we can efficiently filter out the unwanted population and push the target resonator conditionally toward the desired Fock state. In the ideal situation, a Fock state $|n_t\approx2000\rangle$ can be prepared with a fidelity over $98\%$ using only eight rounds of measurements. Under qubit dissipation and dephasing and cavity decay in the current circuit-QED platforms, a Fock state $|n_t\approx100\rangle$ can be prepared with a fidelity of about $80\%$ by six measurements. It is found that the number of measurement rounds for preparing a large Fock state $|n_t\rangle$ scales roughly as $\log_2\sqrt{n_t}$, which is similar to the number of ancillary qubits required in the state preparation via the quantum phase estimation algorithm and yet costs much less in gate operations. Our protocol can also be used to prepare a large Dicke state $|J\simeq1000,0\rangle$ of a spin ensemble with a sufficiently high fidelity by less than six measurements. It is qualified by the quantum Fisher information approaching the Heisenberg scaling in sensing the rotation phase along the $x$ axis.

DOI
10.1103/y4gs-7wt5

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Nonclassical states of bosonic modes, especially the large number states, are valuable resources for quantum information processing and quantum metrology. It is however intricate to generate a desired Fock state of bosonic systems by unitary protocols due to their uniform energy spectrum. We here propose a nonunitary protocol that is based on the resonant Jaynes-Cummings interaction of the bosonic mode with an ancillary two-level atom and sequential projective measurements on the atom. Using the generalized parity-measurement operator constructed by several rounds of free evolution with stepwise halved intervals and measurement, we can efficiently filter out the unwanted population and push the target resonator conditionally toward the desired Fock state. In the ideal situation, a Fock state ∣nt≈2000⟩|n_t\approx2000\rangle∣nt​≈2000⟩ can be prepared with a fidelity over 98%98\%98% using only eight rounds of measurements. Under qubit dissipation and dephasing and cavity decay in the current circuit-QED platforms, a Fock state ∣nt≈100⟩|n_t\approx100\rangle∣nt​≈100⟩ can be prepared with a fidelity of about 80%80\%80% by six measurements. It is found that the number of measurement rounds for preparing a large Fock state ∣nt⟩|n_t\rangle∣nt​⟩ scales roughly as log⁡2nt\log_2\sqrt{n_t}log2​nt​​, which is similar to the number of ancillary qubits required in the state preparation via the quantum phase estimation algorithm and yet costs much less in gate operations. Our protocol can also be used to prepare a large Dicke state ∣J≃1000,0⟩|J\simeq1000,0\rangle∣J≃1000,0⟩ of a spin ensemble with a sufficiently high fidelity by less than six measurements. It is qualified by the quantum Fisher information approaching the Heisenberg scaling in sensing the rotation phase along the xxx axis.
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Large Fock states are important resources for bosonic quantum information and quantum-enhanced metrology, but preparing them with high probability at large excitation numbers remains challenging, as deterministic methods become increasingly control-intensive, while measurement-based approaches typically suffer from low heralding probabilities. Here we propose a protocol that combines quantum nondemolition photon-number encoding with quantum amplitude amplification to enable high-probability heralded generation of large Fock states. Starting from a cavity mode prepared in a coherent state, Quantum Phase Estimation encodes photon-number information into a multi-qubit register, while Quantum Amplitude Amplification boosts the probability of a desired target outcome before measurement. The scheme has an immediate implementation in dispersive circuit-QED, but can be analogously adapted to other bosonic platforms with QND photon-number readout, such as cavity-QED. With a register of up to eight qubits, near-deterministic preparation of Fock states with hundreds of excitations is possible. We also show that the protocol can serve as the first stage of an extension toward generating a two-mode NOON state via a conditional beam-splitter operation.
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The scalable preparation of large photon-number (Fock) states is a long-standing frontier in quantum science, with direct implications for quantum metrology and bosonic quantum information processing. Despite substantial progress at small photon numbers, extending state generation to large photon numbers while maintaining high fidelity and operating deterministically remains a significant challenge. Here we demonstrate a scalable and experimentally accessible control protocol for generating large photon-number states using only native spin--oscillator operations. The protocol alternates Jaynes--Cummings interactions with phase-space displacements to imprint photon-number--dependent phases and convert them into selective interference in photon-number space. It already achieves high preparation fidelity unconditionally, while an optional final qubit projection removes residual qubit--field correlations and further enhances the fidelity. Conditioned on this final projection, photon-number state preparation with fidelities exceeding 0.950.950.95 is achieved for photon numbers in the few-hundred regime, with a success probability exceeding 0.900.900.90, placing the protocol in a near-deterministic operating regime. The resulting control sequences remain shallow and are robust against detuning, control noise, and experimentally relevant dissipation. Our results establish a practical route to scalable, high-fidelity photon-number state preparation at large photon numbers and provide a versatile interference-engineering toolbox for nonclassical bosonic state synthesis.
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