Position Measurements Obeying Momentum Conservation

Abstract

We present a hitherto unknown fundamental limitation to a basic measurement: that of the position of a quantum object when the total momentum of the object and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase (WAY) theorem, and shows that accurate position measurements are only practically feasible if there is a large momentum uncertainty in the apparatus.

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Conservative Quantum Computing
• Conservation laws, uncertainty relations, and quantum limits of measurements
• Gate fidelity of arbitrary single-qubit gates constrained by conservation laws
• Intrinsic unsharpness and approximate repeatability of quantum measurements

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• Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off
• 'Measurement of Quantum Mechanical Operators' Revisited
• Post-selection and quantum energetics
• A relational perspective on the Wigner-Araki-Yanase theorem
• Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
• Heisenberg's uncertainty relation: Violation and reformulation
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Measurement disturbance and conservation laws in quantum mechanics
• Perspective-neutral approach to quantum frame covariance for general symmetry groups
• WAY beyond conservation laws
• On Relativistic Entanglement and Localization of Particles and on their Comparison with the Non-Relativistic Theory
• A quantum reference frame size-accuracy trade-off for quantum channels
• Non-Heisenbergian quantum mechanics