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Multidimensional entropic uncertainty relation based on a commutator matrix in position and momentum spaces
Anaelle Hertz, Luc Vanbever, Nicolas J. Cerf
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two -uples of canonically conjugate variables $(x_…
Boson sampling with Gaussian measurements
Levon Chakhmakhchyan, Nicolas J. Cerf
We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such…
Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states
Anaelle Hertz, Michael G. Jabbour, Nicolas J. Cerf
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon informat…