dorsal/arxiv
View SchemaSum Uncertainty Relation in Quantum Theory
| Authors | A. K. Pati, P. K. Sahu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608092 |
| URL | https://arxiv.org/abs/quant-ph/0608092 |
| DOI | 10.1016/j.physleta.2007.03.005 |
Abstract
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the quantum mechanical uncertainty in any observable is a convex function. We prove that if we have a finite number $N$ of identically prepared quantum systems, then a joint measurement of any observable gives an error $\sqrt N$ less than that of the individual measurements. This has application in quantum metrology that aims to give better precision in the parameter estimation. Furthermore, this proves that a quantum system evolves slowly under the action of a sum Hamiltonian than the sum of individuals, even if they are non-commuting.
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"abstract": "We prove a new sum uncertainty relation in quantum theory which states that\nthe uncertainty in the sum of two or more observables is always less than or\nequal to the sum of the uncertainties in corresponding observables. This shows\nthat the quantum mechanical uncertainty in any observable is a convex function.\nWe prove that if we have a finite number $N$ of identically prepared quantum\nsystems, then a joint measurement of any observable gives an error $\\sqrt N$\nless than that of the individual measurements. This has application in quantum\nmetrology that aims to give better precision in the parameter estimation.\nFurthermore, this proves that a quantum system evolves slowly under the action\nof a sum Hamiltonian than the sum of individuals, even if they are\nnon-commuting.",
"arxiv_id": "quant-ph/0608092",
"authors": [
"A. K. Pati",
"P. K. Sahu"
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"quant-ph"
],
"doi": "10.1016/j.physleta.2007.03.005",
"title": "Sum Uncertainty Relation in Quantum Theory",
"url": "https://arxiv.org/abs/quant-ph/0608092"
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