Quantum metrology: Heisenberg limit with bound entanglement

Quantum metrology allows for a huge boost in the precision of parameters estimation. However, it seems to be extremely sensitive on the noise. Bound entangled states are states with large amount of noise what makes them unusable for almost all quantum informational tasks. Here we provide a counterintuitive example of a family of bound entangled states which can be used in quantum enhanced metrology. We show that these states give advantage as big as maximally entangled states and asymptotically reach the Heisenberg limit. Moreover, entanglement of the applied states is very weak which is reflected by its so called unlockability poperty. Finally, we find instances where behaviour of Quantum Fisher Information reports presence of bound entanglement while a well-known class of strong correlation Bell inequality does not. The question rises of whether (and if so, then to what degree) violation of local realism is required for the sub-shot noise precision in quantum metrology.

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