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Sum Uncertainty Relation in Quantum Theory
A. K. Pati, P. K. Sahu
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0608092
- categories:
- quant-ph
- comments:
- LaTeX file, no figure, 4 pages
- doi:
- 10.1016/j.physleta.2007.03.005
- arxiv_id:
- quant-ph/0608092
- created:
- 2006-08-10
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