Abstract
The maximally-entangled NOON state does not achieve optimal phase sensitivity when N > 4, rather, the Holland-Burnett state is optimal. We experimentally demonstrate this enhanced sensitivity using the six-photon Holland-Burnett state.
Highlights
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit
That work suggested that the uncertainty limit of phase resolution might be achieved by measuring only the probability of the equal photon number output [18]. This is a significant feature of the HB state that makes it more suitable for single fringe phase estimations than the NOON state
For NOON states of any photon number, the optimal phase sensitivity is obtained from a two-outcome measurement that assigns a value of +1 to even photon numbers in the outputs, and −1 to odd photon numbers in the output
Summary
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. Photon statistics appear to limit the sensitivities of N -p√hoton interferometry to phase uncertainties of ∆φ = 1/ N This shot noise limit (SNL) can be overcome by entangling the photons in a single, fully quantum-coherent state [3, 5]. A more favourably-scaling scheme has been demonstrated for postselecting NOON states from entangled states of uncertain photon number [12, 13], but this method is still technically difficult since it requires phase-stabilized interference between two very different light sources. Heralded generation [14] and amplification [15] of path-entangled states have been demonstrated, again for small N
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