Recently, there have been significant developments in entanglement-based quantum metrology. However, entanglement is fragile against experimental imperfections, and quantum sensing to beat the standard quantum limit in scaling has not yet been achieved in realistic systems. Here, we show that it is possible to overcome such restrictions so that one can sense a magnetic field with an accuracy beyond the standard quantum limit even under the effect of decoherence, by using a realistic entangled state that can be easily created even with current technology. Our scheme could pave the way for the realizations of practical entanglement-based magnetic field sensors.

We discuss collapse and revival of Rabi oscillations in a system comprising a qubit and a "big spin" (made of N qubits, or spin-1/2 particles). We demonstrate a regime of behaviour analogous to conventional collapse and revival for a qubit-field system, employing spin coherent states for the initial state of the big spin. These dynamics can be used to create a cat state of the big spin. Even for relatively small values of N , states with significant potential for quantum metrology applications can result, giving sensitivity approaching the Heisenberg limit.

Squeezed states of spin systems are an important entangled resource for quantum technologies, particularly quantum metrology and sensing. Here we consider the generation of spin squeezed states by interacting the spins with a dissipative ancillary system. We show that spin squeezing can be generated in this model by two different mechanisms: one-axis twisting (OAT) and driven collective relaxation (DCR). We can interpolate between the two mechanisms by simply adjusting the detuning between the dissipative ancillary system and the spin system. Interestingly, we find that for both mechanisms, ancillary system dissipation need not be considered an imperfection in our model, but plays a positive role in spin squeezing. To assess the feasibility of spin squeezing we consider two different implementations with superconducting circuits. We conclude that it is experimentally feasible to generate a squeezed state of hundreds of spins either by OAT or by DCR.   r á ñ = J J Tr s , whereˆ(ˆˆˆ)  = J J J J , , x y z is a vector of operators. We denote the unit vector in the direction of the mean spin asˆ|ˆ|    = á ñ á ñ n J J . We quantify spin squeezing of a state r s with the Wineland squeezing parameter [10] |ˆ| ( ·ˆ) ( )     x = á ñN J n J min Var , 1 n 2 2 New J. Phys. 18 (2016) 053011 S Dooley et al N 1 4 s for states r s in the = j N 2 eigenspace of the operatorˆˆˆ= + + J J J J x y z 2 2 2 2 . For each of these

There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in an entangled state can, in principle, lead to a precision gain compared to a probe prepared in a separable state. Even in the presence of some forms of decoherence, it has been shown that the precision gain can increase with the number of probe particles N . Usually, however, the entangled and separable state preparation and readout times are assumed to be negligible. We find that a probe in a maximally entangled (GHZ) state can give an advantage over a separable state only if the entangled state preparation and readout times are lower than a certain threshold. When the probe system suffers dephasing, this threshold is much lower (and more difficult to attain) than it is for an isolated probe. Further, we find that in realistic situations the maximally entangled probe gives a precision advantage only up to some finite number of probe particles N cutoff that is lower for a dephasing probe than it is for an isolated probe.