NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.
1] Steklov Mathematical Institute, 119991 Moscow, Russia [2] National Research University Higher School of Economics (HSE), 101000 Moscow, Russia.
Nat Commun. 2014 May 8;5:3826. doi: 10.1038/ncomms4826.
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.
量子通信理论探索了量子力学对信息传输任务的影响。许多物理信道可以形式化为作用在玻色量子态上的量子高斯操作。根据输入状态和信道质量，输出会受到一定程度的噪声干扰。长期以来，人们一直猜测，但从未证明过，对应于相干输入信号的高斯信道的输出状态是噪声较小的状态（在占优准则的意义上）。在这里，我们证明了这个猜想。具体来说，我们表明，相位不敏感高斯信道的每个输出状态都可以被相干输入对应的输出状态占优。证明基于相干态在严格凹输出泛函的最小化中的最优性。此外，我们还表明，相干态是唯一的最优解。
