The uncertainty constants: A unified framework of two, three and four observables

• URL: http://arxiv.org/abs/2512.24950v1
• Date: Wed, 31 Dec 2025 16:31:07 GMT
• Title: The uncertainty constants: A unified framework of two, three and four observables
• Abstract summary: Uncertainty is a fundamental and important concept in quantum mechanics.<n>Recent works have revealed both the product and sum forms of uncertainty constants for three observables.<n>We give an alternative proof for the case of three observables, and generalize the result to the case of four measurements.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Uncertainty is a fundamental and important concept in quantum mechanics. Recent works have revealed both the product and sum forms of uncertainty constants for three observables. Such a result is intimately to the properties of Pauli operators. In this work, using the technique in matrix theory, we give an alternative proof for the case of three observables, and generalize the result to the case of four measurements. Comparing with the original proof, such a derivation is simplified. Moreover, the discussions can deal with the summation form of uncertainty relation for two, three and four observables in a unified way.

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