Abstract：
:We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the "classical" noise-resolution uncertainty limit. This uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum optics and imaging.
journal_name
Sci Repjournal_title
Scientific reportsauthors
Gureyev TE,Kozlov A,Paganin DM,Nesterets YI,Quiney HMdoi
10.1038/s41598-020-64539-7subject
Has Abstractpub_date
2020-05-12 00:00:00pages
7890issue
1issn
2045-2322pii
10.1038/s41598-020-64539-7journal_volume
10pub_type
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