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Two-Mode Bosonic State Tomography with Single-Shot Joint-Parity Measurement of a Trapped Ion

Honggi Jeon*,†, Jiyong Kang†, Wonhyeong Choi, Kyunghye Kim, and Jaehun You

Taehyun Kim‡

  • *Present address: Duke Quantum Center, Duke University, Durham, North Carolina 27701, USA.
  • †These two authors contributed equally to this work.
  • ‡Contact author: taehyun@snu.ac.kr
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PRX Quantum 6, 040352 – Published 3 December, 2025

DOI: https://doi.org/10.1103/wsqr-j9f4

Abstract

The full characterization of a continuous-variable quantum system is a challenging problem. For the trapped-ion system, a number of methods of measuring the quantum states have been developed, including the measurement of the Q quasiprobability function and the density-matrix elements in the Fock basis, but these approaches are often slow and difficult to scale to multimode states. Here, we demonstrate a novel and powerful scheme for measuring a continuous-variable quantum state that uses the direct single-shot measurement of the joint parity of the phonon states of a trapped ion. We drive a spin-dependent bichromatic beam-splitter interaction that coherently exchanges phonons between different harmonic oscillator modes of the ion. This interaction encodes the joint-parity information into the relative phase between the two spin states, enabling measurement of the combined phonon-number parity across multiple modes in a single shot. Leveraging this capability, we directly measure multimode Wigner quasiprobability distributions to perform quantum state tomography of an entangled coherent state, and calculate various quantum informational quantities with a model-based estimation of the density matrix. We further show that the single-shot joint-parity measurement can be used to detect parity-flip errors in real time. By postselecting the parity-measurement outcomes, we experimentally demonstrate the partial recovery of coherence, effectively implementing an error-mitigation technique. Lastly, we identify the various sources of error affecting the fidelity of the spin-dependent beam-splitter operation and study the feasibility of high-fidelity operations. The interaction studied in this work can be extended to more than two modes, and is highly relevant to continuous-variable quantum computing and quantum metrology.

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Popular Summary

Quantum states can be described not only by discrete variables, such as the spin of a particle, but also by continuous variables, such as position and momentum. These continuous-variable quantum states offer powerful new capabilities for quantum computing, communication, and metrology, complementing traditional approaches based on discrete quantum systems. However, characterizing such states—especially when multiple modes are entangled—is notoriously challenging and typically requires large numbers of repeated measurements.

In this work, we experimentally demonstrate a new method for efficiently measuring multimode continuous-variable quantum states. A pair of laser beams is used to couple the internal spin state of the ion to its quantized motional state that provides a discrete representation of a continuous-variable system. This interaction allows us to measure the joint parity by determining whether the total number of vibrational quanta across two motional modes is even or odd, all in a single experimental shot.

Using this spin-dependent interaction, we perform full state characterization of various multimode quantum states, including entangled coherent states. We also show that this method can detect and reject certain types of noise that degrade the state, providing a pathway toward bosonic quantum error correction based on parity detection.

The technique demonstrated here is fast, nondestructive, and scalable to more motional modes. It opens up the new possibilities of quantum computing architectures and holds promise for quantum metrology, where parity measurements can offer enhanced sensitivity.

Article Text

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PRX Quantum 6, 040352– Published 3 December, 2025
  • Received 23 June 2025
  • Accepted 22 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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