Quantum Asymmetry and Noisy Multimode Interferometry

Quantum asymmetry is a physical resource that coincides with the amount of coherence between the eigenspaces of a generator responsible for phase encoding in interferometric experiments. We highlight an apparently counterintuitive behavior that the asymmetry may increase as a result of a decrease of coherence inside a degenerate subspace. We intuitively explain and illustrate the phenomena by performing a three-mode single-photon interferometric experiment, where one arm carries the signal and two noisy reference arms have fluctuating phases. We show that the source of the observed sensitivity improvement is the reduction of correlations between these fluctuations and comment on the impact of the effect when moving from the single-photon quantum level to the classical regime. Finally, we also establish the analogy of the effect in the case of entanglement resource theory.

Figure 1

Schematics of the experimental demonstration of phase estimation in the three-arm interferometer with correlated noise. Heralded single photons from spontaneous parametric down-conversion are used to probe the system with noisy phases ${\varphi }_1$ and ${\varphi }_2$ to estimate the phase $\theta$. Inset shows an example realization of phase noise with high anticorrelation.

Figure 2

(a)–(d) Exemplary probability distributions for two different $\eta$ settings in the perfectly correlated and anticorrelated case. The points correspond to measured and renormalized coincidences ($\tilde{N}$). (e) Measured (points) and expected (solid lines) visibility parameter for chosen $\eta$ and $c$ parameters.

Figure 3

Precision of $\theta$ estimation (points) for set of $\eta$ and $c$ parameters compared with CRB and QCRB given by FI (solid lines) and QFI, respectively.