title: Quantum state majorization at the output of bosonic Gaussian channels.
abstract: Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states. Depending on the input state and on the quality of the channel, the output suffers certain amount of noise. For a long time it has been conjectured, but never proved, that output states of Gaussian channels corresponding to coherent input signals are the less noisy ones (in the sense of a majorization criterion). Here we prove this conjecture. Specifically we show that every output state of a phase-insensitive Gaussian channel is majorized by the output state corresponding to a coherent input. The proof is based on the optimality of coherent states for the minimization of strictly concave output functionals. Moreover we show that coherent states are the unique optimizers.
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Mari
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.
authors.forename: V
authors.initials: V
authors.lastname: Giovannetti
authors.affiliation: 1] Steklov Mathematical Institute, 119991 Moscow, Russia [2] National Research University Higher School of Economics (HSE), 101000 Moscow, Russia.
authors.forename: A S
authors.initials: AS
authors.lastname: Holevo