Theory of direct measurement of the quantum pseudo-distribution via its characteristic function
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917252308140032 |
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| author | Jordan, Andrew N. Arvidsson-Shukur, David R. M. Steinberg, Aephraim M. |
| author_facet | Jordan, Andrew N. Arvidsson-Shukur, David R. M. Steinberg, Aephraim M. |
| contents | We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extracted from the data in a theory-agnostic way, it is shown that under quantum-mechanical formalism, the predicted pseudo-distribution is identified with the Kirkwood-Dirac pseudo-distribution. We discuss the construction of both the joint pseudo-distribution and a conditional pseudo-distribution, which is closely connected to weak-value physics. By permuting position and momentum measurements, we give a prescription to directly probe the canonical commutation relation and verify it for any quantum state. This work establishes the theory of a characteristic function approach to pseudo-distributions, as well as providing a constructive approach to measuring them directly. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theory of direct measurement of the quantum pseudo-distribution via its characteristic function Jordan, Andrew N. Arvidsson-Shukur, David R. M. Steinberg, Aephraim M. Quantum Physics Optics We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extracted from the data in a theory-agnostic way, it is shown that under quantum-mechanical formalism, the predicted pseudo-distribution is identified with the Kirkwood-Dirac pseudo-distribution. We discuss the construction of both the joint pseudo-distribution and a conditional pseudo-distribution, which is closely connected to weak-value physics. By permuting position and momentum measurements, we give a prescription to directly probe the canonical commutation relation and verify it for any quantum state. This work establishes the theory of a characteristic function approach to pseudo-distributions, as well as providing a constructive approach to measuring them directly. |
| title | Theory of direct measurement of the quantum pseudo-distribution via its characteristic function |
| topic | Quantum Physics Optics |
| url | https://arxiv.org/abs/2602.06145 |