On possible extensions of quantum mechanics

• URL: http://arxiv.org/abs/2512.06964v1
• Date: Sun, 07 Dec 2025 19:04:50 GMT
• Title: On possible extensions of quantum mechanics
• Authors: Yiruo Lin,
• Abstract summary: It was argued that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen.<n>I show that the measurement assumption can be further relaxed without affecting the conclusion on the predictive power of quantum mechanics versus alternative theories.
• Score: 0.4873362301533824
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It was argued [1] that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen, independently of any event that is not in its future light cone. The assumption of measurement choice was criticized [2] to be too strong to be physically necessary and extensions of quantum mechanics were shown [3] to be possible under a more relaxed measurement assumption. Here I point out an error in the criticism and observe that the actual mistake of the no-go theorem lies in an unwarranted assumption implicitly made in the proof of [1]. Hence, quantum mechanics is guaranteed to have the maximal predictive power only in situations of complete certainty and complete uncertainty about measurement outcomes. I then show that the measurement assumption can be further relaxed without affecting the conclusion on the predictive power of quantum mechanics versus alternative theories. I further study the optimal predicative improvement over quantum mechanics of local spin measurements on a pair of entangled qubits by any alternative theory and conjecture a strict upper bound.

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