Abstract
We use Rényi-entropy-power-based uncertainty relations to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is analogous to quantum-state tomography. We illustrate our point with the so-called “cat states”, which are of both fundamental interest and practical use in schemes such as quantum metrology, but are not well described by standard variance-based approaches.
Highlights
There has been a recent upsurge of interest in quantum-mechanical (QM) uncertainty relations (URs) catalyzed by new ideas from information theory [1, 2, 3, 4, 5], functional analysis [6, 7] and cosmology [8, 9, 10] as well as experiments that have observed violations of Heisenberg’s error-disturbance uncertainty relations [11, 12, 13, 14, 15]
In the first part of this paper we have presented a new proof of a one-parameter class of Renyi-entropy-power-based URs for pairs of observables in an infinite-dimensional Hilbert space
The mathematical language employed in the new proof (i.e., Fisher information matrix, Cramer– Rao inequality, etc.) is much closer to the language familiar in quantum information theory and, in particular, quantum metrology, and so makes stronger connections to these fields
Summary
There has been a recent upsurge of interest in quantum-mechanical (QM) uncertainty relations (URs) catalyzed by new ideas from (quantum) information theory [1, 2, 3, 4, 5], functional analysis [6, 7] and cosmology [8, 9, 10] as well as experiments that have observed violations of Heisenberg’s error-disturbance uncertainty relations [11, 12, 13, 14, 15]. We use Renyi-entropy-power-based uncertainty relations to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is analogous to quantum-state tomography. De Bruin’s identity: Let {Xi} be a random vector in RD with the PDF F (x) and let {ZiG} be a Gaussian noise vector with zero mean and unit-covariance matrix, independent of {Xi}.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
