The use of an interferometer to perform an ultra-precise parameter estimation under noisy conditions is a challenging task. Here we discuss nearly optimal measurement schemes for a well known, sensitive input state, squeezed vacuum and coherent light. We find that a single mode intensity measurement, while the simplest and able to beat the shot-noise limit, is outperformed by other measurement schemes in the low-power regime. However, at high powers, intensity measurement is only outperformed by a small factor. Specifically, we confirm, that an optimal measurement choice under lossless conditions is the parity measurement. In addition, we also discuss the performance of several other common measurement schemes when considering photon loss, detector efficiency, phase drift, and thermal photon noise. We conclude that, with noise considerations, homodyne remains near optimal in both the low and high power regimes. Surprisingly, some of the remaining investigated measurement schemes, including the previous optimal parity measurement, do not remain even near optimal when noise is introduced.

In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put vacuum into one input port of a balanced Mach-Zehnder Interferometer, then no matter what you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the shot noise limit (SNL). Often the proof of this theorem is cited to be in Ref. [C. Caves, Phys. Rev. D 23, 1693(1981], but upon further inspection, no such claim is made there. A quantum-Fisher-information-based argument suggestive of this no-go theorem appears in Ref. [M. Lang and C. Caves, Phys. Rev. Lett. 111, 173601 (2013)], but is not stated in its full generality. Here we thoroughly explore this no-go theorem and give the rigorous statement: the nogo theorem holds whenever the unknown phase shift is split between both arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications.Introduction.-In the field of quantum metrology [1][2][3], a Mach-Zehnder interferometer (MZI) is a tried and true workhorse that has the additional advantage that any result obtained for it also applies to a Michelson interferometer (MI) and hence has a potential application to gravitational wave detection. In most current implementations of gravitational wave detectors, the MI is fed with a strong coherent state of light in one input port and vacuum in the other (Fig. 1). It was in this context that Caves in 1981 [4] showed that such a design would always only ever achieve the shotnoise limit (SNL). Then he showed if you put squeezed vacuum into the unused port, you could beat the SNL. Several implementations of this squeezed vacuum scheme have already been demonstrated in the GEO 600 gravitational detector, and plans are underway to utilize this approach in the LIGO and VIRGO detectors in the future [5,6].It then appeared, that in the lore of quantum metrology, this result was extended -without proof -to the following no-go theorem: If you put quantum vacuum into one input port of a balanced MZI, then no matter what quantum state of light you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the SNL. Often the proof of this theorem is cited to be the original 1981 paper by Caves [4], but upon further inspection, no such general claim is made there. A quantum-Fisherinformation-based argument suggestive of this no-go theorem appeared in Ref. [7] by Lang and Caves, but it does not explore the statement in adequate generality.In this work, we give a full statement of the no-go theorem. The statement proved here is the following: if the unknown phase shifts are in both of the two arms of the MZI, then the no-go theorem holds no matter whether the MZI is balanced or not. However, in the case where the unknown phas...

The identification of light sources represents a task of utmost importance for the development of multiple photonic technologies. Over the last decades, the identification of light sources as diverse as sunlight, laser radiation, and molecule fluorescence has relied on the collection of photon statistics or the implementation of quantum state tomography. In general, this task requires an extensive number of measurements to unveil the characteristic statistical fluctuations and correlation properties of light, particularly in the low-photon flux regime. In this article, we exploit the self-learning features of artificial neural networks and the naive Bayes classifier to dramatically reduce the number of measurements required to discriminate thermal light from coherent light at the single-photon level. We demonstrate robust light identification with tens of measurements at mean photon numbers below one. In terms of accuracy and number of measurements, the methods described here dramatically outperform conventional schemes for characterization of light sources. Our work has important implications for multiple photonic technologies such as light detection and ranging, and microscopy.

The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we demonstrate that the manipulation of the quantum electromagnetic fluctuations of a pair of vacuum states leads to a novel family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on the use of conditional measurements to engineer the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. The experimental generation of multiphoton states with quantum correlations by means of photon subtraction unveils novel mechanisms to control fundamental properties of light. As a remarkable example, we demonstrate the engineering of a quantum correlated state of light, with nearly Poissonian photon statistics, that constitutes the first step towards the generation of entangled lasers. Our technique enables a robust protocol to prepare quantum states with multiple photons in high-dimensional spaces and, as such, it constitutes a novel platform for exploring quantum phenomena in mesoscopic systems.The identification of the photon as a fundamental carrier of information has triggered a wide variety of research that aims to improve the state of the art of photonic technologies [1]. Along these lines, the field of quantum photonics has focused on exploiting the quantum properties of light to dramatically improve the performance of protocols for communication, metrology, imaging, and information processing [2-4]. Consequently, the successful implementation of functional quantum photonic technologies hinges on our ability to generate, manipulate, and measure complex multiphoton states [5][6][7]. However, the generation of high-dimensional entangled states comprising a large number of photons is nowadays one of the most challenging tasks in quantum optics [8,9].Over the past few years, physicists and engineers have demonstrated the utilization of multiple degrees of freedom of single photons to perform information processing tasks for a wide range of applications. In this regard, multiple bits of information have successfully been encoded in a single photon by preparing complex superpositions in time, frequency, position, transverse momentum, angular position, orbital angular momentum and path [10][11][12][13][14][15]. The complexity of such superpositions has led to important improvements in the performance and tolerance of cryptographic protocols, in the estimation of small physical parameters, and in the development of novel schemes for information processing [1][2][3][4]. Furthermore, it is now recognized that such protocols can be further improved by incorporating a high number of pho-tons, correlated and entangled [16][17][18][19]. Interestingly, the generation...