It is well-known that the super-sensitivity of phase estimation in two-photon interferometery is diminished by the effect of decoherence. Specific to the paradigm of local phase estimation, any presence of decoherence removes all sensitivity to small shifts in the neighborhood of certain phases. For estimates of the phase difference between two arms of an interferometer using two-photon coincidence measurements, all sensitivity is lost for phase differences in the neighborhood of π/2. The benefit of employing an ancillary optical degree of freedom alongside the principal interfering degree of freedom was recently found to fortify super-sensing two-photon states against the debilitating effect of spectral distinguishability: an effect that reduces the visibility of two-photon interference. In the present work, we investigate the use of an ancillary degree of freedom when measuring a phase shift by use of a two-photon Mach-Zehnder-interferometer contaminated by a depolarizing channel causing decoherence: an effect that reduces both two-photon and single-photon interference visibility. We model our input state as single photons entering both input ports of an interferometer. The principal interferometer-path modes are coupled to polarization, and decoherence is modeled by replacing the density matrix describing this input with a maximally mixed state with some probability p. We calculate the sensitivity through the quantum fisher information, finding that the process of fortifying input states retains sensing at or above the standard quantum limit in the neighborhood of phase differences around π/2, for all probabilities below 1/4 — an advantage impossible without employing the ancillary degree of freedom.
It is well-known that the super-sensitivity of phase estimation in two-photon interferometery is diminished by the effect of decoherence. Specific to the paradigm of local phase estimation, any presence of decoherence removes all sensitivity to small shifts in the neighborhood of certain phases. For estimates of the phase difference between two arms of an interferometer using two-photon coincidence measurements, all sensitivity is lost for phase differences in the neighborhood of π/2. The benefit of employing an ancillary optical degree of freedom alongside the principal interfering degree of freedom was recently found to fortify super-sensing two-photon states against the debilitating effect of spectral distinguishability: an effect that reduces the visibility of two-photon interference. In the present work, we investigate the use of an ancillary degree of freedom when measuring a phase shift by use of a two-photon Mach-Zehnder-interferometer contaminated by a depolarizing channel causing decoherence: an effect that reduces both two-photon and single-photon interference visibility. We model our input state as single photons entering both input ports of an interferometer. The principal interferometer-path modes are coupled to polarization, and decoherence is modeled by replacing the density matrix describing this input with a maximally mixed state with some probability p. We calculate the sensitivity through the quantum fisher information, finding that the process of fortifying input states retains sensing at or above the standard quantum limit in the neighborhood of phase differences around π/2, for all probabilities below 1/4 — an advantage impossible without employing the ancillary degree of freedom.
The super-sensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots -- phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point of the sensor to a less vulnerable phase value. We present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an adaptive estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally super-sensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.
The supersensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots---phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point to a less vulnerable phase value. Since this is not always feasible, we present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally supersensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.
Recent advances in quantum photonics have enabled increasingly robust protocols in optical phase estimation, achieving precisions beyond the standard quantum limit and approaching the Heisenberg limit. While intrinsic losses hinder the realization of unconditional super-sensitivity, reaching quantum advantage, defined as sensitivity surpassing that of any classical counterpart with identical resources, remains achievable. Here we experimentally demonstrate such an advantage using a fully fibered Mach-Zehnder-type interferometer operating at telecom wavelengths, free of post-selection. The scheme relies on the conversion of polarization-entangled photon pairs, a degree of freedom commonly favored for experimental convenience, into energy-time entanglement, which is particularly well suited for scalable fiber-based sensors. All system imperfections, including asymmetric losses and detector inefficiencies, are accounted for in the Fisher information analysis, yielding a measured quantum advantage of 10%. This result highlights the practicality of compact, alignment-free quantum interferometers for real-world sensing applications.
The insights offered by quantum mechanics to the field of optical metrology are many-fold, with non-classical states of light themselves used to make sensors that surpass the sensitivity of sensors using classical states of light. Unfortunately, this advantage, referred to often as "super-sensitivity" is notoriously fragile, and even the slightest experimental imperfections may greatly reduce the efficacy of the non-classical sensors, sometimes completely obviating their advantage. In my thesis I have shown that the performance of an otherwise ideal two-photon interferometer, which exploits entanglement between photons to make super-sensitive measurements of phase, is crippled by the slightest introduction of decoherence between modes of the interferometer. I have shown further that such drastic reduction in sensitivity can also appear in classical measurement problems, specifically that the recently developed methods of estimating the separation between a pair of point sources are rendered less effective when the ideal assumption of complete spatial incoherence is relaxed. Towards overcoming these and other issues, I have designed new configurations that use ancillary optical degrees of freedom, a tool-set that has recently garnered much interest in the field of quantum optics. In the context of two-photon interferometry, I have shown that by coupling polarization to the spatial-structure of the two photon state used to probe phase it is possible to obviate the need for a reference phase, even in the context of decoherence and imperfections in the interferometer. In the context of two-point resolution, I have developed an anisotropic imaging system that performs the function of an image-inversion interferometer and is inherently stable, offering an attractive implementation of recently developed methods of sub-Rayleigh imaging. I have further shown both theoretically and experimentally that the same anisotropic image-inversion interferometer is useful in measuring spatially encoded phases, both in the context of classical illumination as well as quantum-aided two-photon super-sensing. In both cases, the ability to perform interferometric measurements of the spatial structure of an electric field without splitting beam paths forms a bridge between conception and implementation of precision-sensing measurement strategies. Finally, I have shown that binary interferometric method based on the common-path anisotropic imaging system that I introduced, are able to measure both phase gradients and transverse beam tilts with a sensitivity beating conventional systems that are used both commercially and in research laboratories.
We consider Mach-Zehnder and Hong-Ou-Mandel interferometers with nonclassical states of light as input, and study the effect that dispersion inside the interferometer has on the sensitivity of phase measurements. We study in detail a number of different one- and two-photon input states, including Fock, dual Fock, maximally path-entangled $\ensuremath{\mid}N,0⟩+⟨{0}_{,}N\ensuremath{\mid}$ (``N00N'') states, and photon pairs from parametric down-conversion. Assuming there is a phase shift ${\ensuremath{\phi}}_{0}$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of ${\ensuremath{\phi}}_{0}$, and then compute the Shannon mutual information between ${\ensuremath{\phi}}_{0}$ and the measurements. This provides a means of quantitatively comparing the utility of various input states for determining the phase in the presence of dispersion. In addition, we consider a simplified model of parametric down-conversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic down-conversion model.