Quantum state majorization at the output of bosonic Gaussian channels
Quantum state majorization at the output of bosonic Gaussian channels
复制标题
玻色高斯通道输出处的量子态主化
作者：
A. Mari;V. Giovannetti;A. Holevo
量子通信理论探索了量子力学对信息传输任务的影响。许多物理通道可以形式化地描述为作用于玻色量子态的量子高斯运算。根据输入状态和通道质量的不同，输出会受到一定程度的噪声。很长一段时间以来，人们一直猜测，与相干输入信号对应的高斯信道的输出状态是噪声较小的(在优化准则意义上)，但从未得到证明。在这里，我们证明了这个猜想。具体地说，我们证明了相位不敏感高斯信道的每个输出态都被对应于相干输入的输出态所支配。证明是基于严格凹输出泛函最小化的相干态的最优性。此外，我们还证明相干态是唯一的优化器。在量子信息学中，占优猜想指出，量子高斯通道输出端的最小无序量是由相干输入态产生的，但它的证明仍然难以捉摸。现在，Mari等人解决了这个长期存在的问题，并强调了它的一些影响。
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. In quantum information the majorization conjecture states that the minimum amount of disorder at the output of a quantum Guassian channel is produced by coherent input states, but its proof has remained elusive. Now, Mari et al.solve this longstanding problem and highlight some of its implications.