Abstract
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N + 1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SNL have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investigate the achievable phase sensitivity of the simple and efficient single interference fringe detection technique. We show that the maximally-entangled “NOON” state does not achieve optimal phase sensitivity when N > 4, rather, we show that the Holland-Burnett state is optimal. We experimentally demonstrate this enhanced sensitivity using a single photon-counted fringe of the six-photon Holland-Burnett state. Specifically, our single-fringe six-photon measurement achieves a phase variance three times below the SNL.
Highlights
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit
Since much of the theory of quantum metrology has focussed on the properties of the input state, it is often implicitly assumed that the optimal measurement strategy for a given input state can be implemented with available technologies
For NOON states of any photon number, the optimal phase sensitivity is obtained from a two-outcome measurement that assigns a value of 11 to even photon numbers in the outputs, and 21 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. Recent experimental demonstrations of precision beyond the SNL have used only one or two photon-number detection patterns instead of parity measurements. Her.e,pphffiffiffioffi ton statistics appear to limit the sensitivities of N-photon interferometry to phase uncertainties of Dw~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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