Temporal inequalities for sequential multi-time actions in quantum information processing

Marek Żukowski

Marek, Zukowski

时间的不平等的一种新类型被讨论，它适用于算法的进程，包含处理联合起来的有限记忆。他们是 Leggett-Grag，以及到由 Brukner 等的修改的一种选择。如果一个人考虑包含有限存储器的系统的量和古典进程的比较(在两个盒子中的一样的能力) ，不平等给我们能期望量加速的一条清楚的消息。在古典进程，一个人清楚地总是定义可能的大小的值，或以信息处理语言如果我们有一取决于到达各个的数据的某功能的顺序的计算走在一个算法上，函数总是有清楚地定义的值。在算法的结束以后，在量盒子中，仅仅最后的价值被定义。与 Bohrs 补充一致，所有中间的价值不能被归功于明确的价值。

Marek Żukowski

A new kind of temporal inequalities are discussed, which apply to algorithmic processes, involving a finite memory processing unit. They are an alternative to the Leggett-Grag ones, as well as to the modified ones by Brukner et al . If one considers comparison of quantum and classical processes involving systems of finite memory (of the same capacity in both cases), the inequalities give a clear message why we can expect quantum speed-up. In a classical process one always has clearly defined values of possible measurements, or in terms of the information processing language, if we have a sequential computations of some function depending on data arriving at each step on an algorithm, the function always has a clearly defined value. In the quantum case only the final value, after the end of the algorithm, is defined. All intermediate values, in agreement with Bohr’s complementarity, cannot be ascribed a definite value.

A Frigerio

E. B. Davies

Marek Żukowski

The usual formulation of Macrorealism is recast to make this notion fully concurrent with the basic ideas behind classical physics. The assumption of non-invasiveness of measurements is dropped. Instead, it is assumed that the current state of the system defines full initial conditions for its subsequent evolution. An example of a new family of temporal Bell inequalities is derived which can be applied to processes in which the state of the system undergoes arbitrarily many transformations (which was not the case in the original approach). An exponential (in terms of number of operations) violation of this inequality is demonstrated theoretically. Finally it is shown that such inequalities were indirectly tested in a 2005 experiment by the Weinfurter group.