Abstract
Quantum metrology calculates the ultimate precision of all estimation strategies, measuring what is their root-mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover; namely, we derive an information-theoretic quantum metrology. In this setting, we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in the quantum estimation theory) and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based one.
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