Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight
Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight
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DOI：
10.1103/physrevlett.103.160502
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发表时间：
2009-10-16
影响因子：
8.6
通讯作者：
Toffoli, Tommaso
中科院分区：
文献类型：
--
作者：
Levitin, Lev B.;Toffoli, Tommaso
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。基于能量扩展Δ E的正交化时间的下限由Mandelovite和Tamm发现。另一个基于平均能量E的界限是由马戈卢斯和列维京建立的。当Δ E = E时，这两个界是一致的，并且可以由某些初始状态得到.然而，当Δ E不等于E时，问题仍然存在。我们考虑包含Δ E和E的统一界。我们证明了，如果Δ E不等于E，则不存在使边界饱和的初态。然而，边界仍然是紧的：对于任何Δ E和E的值，存在一个单参数的初始状态族，当参数接近其极限时，它可以任意接近边界。这些结果确定了任何信息处理系统运行速度的基本限制。
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 Delta E, 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 Delta E = E. Yet, the problem remained open when Delta E not equal E. We consider the unified bound that involves both Delta E and E. We prove that there exist no initial states that saturate the bound if Delta E not equal E. However, the bound remains tight: for any values of Delta E 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.