Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev Lett. 2009 Oct 16;103(16):160502. doi: 10.1103/PhysRevLett.103.160502. Epub 2009 Oct 13.
How fast a quantum state can evolve has attracted considerable attention in connection with quantum measurement and information processing. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide and can be attained by certain initial states if DeltaE=E. Yet, the problem remained open when DeltaE not equal E. We consider the unified bound that involves both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE not equal E. However, the bound remains tight: for any values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit. These results establish the fundamental limit of the operation rate of any information processing system.
量子态的演化速度在量子测量和信息处理方面引起了相当大的关注。Mandelstam 和 Tamm 基于能量展宽 DeltaE 找到了正交化时间的下限。Margolus 和 Levitin 基于平均能量 E 建立了另一个下限。如果 DeltaE=E，则这两个下限是一致的，可以通过某些初始状态达到。然而，当 DeltaE 不等于 E 时，这个问题仍然没有解决。我们考虑了同时涉及 DeltaE 和 E 的统一界限。我们证明，如果 DeltaE 不等于 E，则不存在达到界限的初始状态。然而，这个界限仍然是严格的：对于 DeltaE 和 E 的任何值，当参数接近其极限时，存在一个参数化的初始状态族，可以任意接近这个界限。这些结果确定了任何信息处理系统的操作速率的基本限制。
