#CLOCKWORK AUTOMATON IN EQ FULL#

Pauli then argued that this implies that H has as its spectrum the full real line Pashby14. Furthermore, since neither T nor the Hamiltonian of the system, H, should depend on time explicitly, they would need to satisfy the commutation relation i = 1.

The observable T would need to satisfy d d t T = 1. Pauli regarded an “ideal clock” as a device that has an observable T whose value is in one-to-one correspondence to the time parameter t in the quantum-mechanical equation of motion. In contrast, for the task of time keeping considered here, the relevant resource is the size of the clock. In computation, the relevant resource is the number of computational steps, and in the case of metrology, it is the number of basic measurement steps. 6 6 6In particular, we are not aware of a result that would allow us to obtain statements like Eqs. ( 1) and ( 2) from known bounds in quantum metrology see Section III.1.2 for more details. However, despite the superficial similarities between these results, they are of a fundamentally different kind, for they refer to different resources. required to determine an experimental parameter to a given precision drops like a square root if one uses quantum instead of classical methods GiLlMa11. In this case one may regard the generation and detection of a single photon as a basic measurement step. Similarly, the number of basic measurement steps 5 5 5A typical example is the measurement of a distance using laser interferometry, where the relevant resource is the energy of the beam or the number of photons that are involved in the measurement process. For example, Grover’s quantum algorithm exhibits a quadratic speed-up compared to any classical algorithm for database search Grover1996.

Other items on this list come from the areas of computation and metrology. This result allows us to add a new item to the list of tasks with a quantum-over-classical advantage - the task of time-keeping.

Clockwork automaton in eq