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Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs

Massimiliano F. Sacchi

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Phys. Rev. A 114, 022466 – Published 26 August, 2026

DOI: https://doi.org/10.1103/bgxx-s3qj

Abstract

We determine the optimal information-disturbance tradeoff for estimating an unknown spatial direction encoded in two antiparallel spins. Rotational covariance reduces the optimization over all instruments to a finite-dimensional Choi problem: a positive seed operator obeys one trace constraint for each irreducible sector of the input representation, while both the directional score and the operation fidelity are linear functionals of this seed. For two antiparallel spin-1/2 particles, whose physical representation decomposes as 0⊕1, we derive the two-multiplier dual problem and characterize the optimal instrument from the kernel vectors of the dual slack operator. The optimal operation is a covariant filter with scalar-vector coherence and is generally not a convex interpolation between the identity channel and a measure-and-reprepare strategy. At maximum information, we recover the Gisin-Popescu score, but the least disturbing output state is optimized independently, giving a smaller disturbance than both the parallel-spin benchmark and antiparallel measure-and-reprepare. We also formulate the parallel benchmark and, as a central extension of the method, treat antiparallel spin-coherent states of arbitrary spin j. In this case the signal coherently occupies all sectors ℓ=0,...,2j of j⊗j, the endpoint information is governed by nearest-neighbor sector coherences, and the endpoint disturbance is obtained from an explicit finite block-diagonal eigenvalue problem.

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Phys. Rev. A 114, 022466– Published 26 August, 2026
  • Received 16 June 2026
  • Accepted 14 August 2026
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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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