We consider the simultaneous measurement of two conjugate variables by coupling the system of interest to two independent probe modes. Our model consists of linearly coupled boson modes that can be realized by quantum optical fields in the rotating-wave approximation. We approach the setup both as a device to extract observable information and to prepare an emerging quantum state. The initial states of the probe modes and the coupling are utilized to optimize the operation in the various regimes. In contrast to the Arthurs and Kelly ideal scheme [Bell. Syst. Tech. J. 44, 725 (1965)], our more realistic coupling does not allow perfect operation but the ideal situations can be approximated closely. We discuss the conditions for maximum information transfer to the probe modes, information extraction with minimum disturbance of the system mode, and optimal state preparation for subsequent measurements. The minimum disturbance operation can be made to approximate a nondemolition measurement, especially when the information is carried in one quadrature component only. In the preparation mode, we find that the recording accuracy of the probe signals plays an essential role. We restrict the discussion to the first and second moments only, but the method can easily be generalized to any situation. Choosing all modes to be in squeezed coherent states originally, we can carry out analytical considerations; other cases can be treated numerically. The results are presented and discussed in detail as the paradigm of a class of realizable measurements.
We consider the simultaneous measurement of two conjugate variables by coupling the system of interest to two independent probe modes. Our model consists of linearly coupled boson modes that can be realized by quantum optical fields in the rotating-wave approximation. We approach the setup both as a device to extract observable information and to prepare an emerging quantum state. The initial states of the probe modes and the coupling are utilized to optimize the operation in the various regimes. In contrast to the Arthurs and Kelly ideal scheme [Bell. Syst. Tech. J. 44, 725 (1965)], our more realistic coupling does not allow perfect operation but the ideal situations can be approximated closely. We discuss the conditions for maximum information transfer to the probe modes, information extraction with minimum disturbance of the system mode, and optimal state preparation for subsequent measurements. The minimum disturbance operation can be made to approximate a nondemolition measurement, especially when the information is carried in one quadrature component only. In the preparation mode, we find that the recording accuracy of the probe signals plays an essential role. We restrict the discussion to the first and second moments only, but the method can easily be generalized to any situation. Choosing all modes to be in squeezed coherent states originally, we can carry out analytical considerations; other cases can be treated numerically. The results are presented and discussed in detail as the paradigm of a class of realizable measurements.
We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to a fully nondestructive noninformative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or antisqueezed probes respectively, one achieves either a projective measurement, i.e., homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or a fully nondestructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase shift of the interferometer, the whole set of intermediate cases may also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature may be achieved, which minimizes the information gain versus state disturbance tradeoff.
The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.
Joint approximate measurement schemes of position and momentum provide us with a means of inferring pieces of complementary information if we allow for the irreducible noise required by quantum theory. One such scheme is given by the Arthurs-Kelly model, where information about a system is extracted via indirect probe measurements, assuming separable uncorrelated probes. Here, following Di Lorenzo [Phys. Rev. Lett. 110, 120403 (2013)], we extend this model to both entangled and classically correlated probes, achieving full generality. We show that correlated probes can produce more precise joint measurement outcomes than the same probes can achieve if applied alone to realize a position or momentum measurement. This phenomenon of focusing may be useful where one tries to optimize measurements with limited physical resources. Contrary to Di Lorenzo's claim, we find that there are no violations of Heisenberg's error-disturbance relation in these generalized Arthurs-Kelly models. This is simply due to the fact that, as we show, the measured observable of the system under consideration is covariant under phase space translations and as such is known to obey a tight joint measurement error relation.
The implementation of optical quantum technologies requires precise and complete characterisation tools for multi-mode nonclassical states of light. In this thesis, we propose and we implement experimentally three applications of optical quantum measurements, which combine aspects of light that are described by both discrete and continuous variables. In the rst part of this thesis, we present a new scheme for interferometric phase estimation, which uses double homodyne measurements as an alternative to photon counting. We show that, without requiring a phase reference, this scheme can achieve the optimum phase estimation precision for all path-symmetric probe states with a de ned number of photons. Furthermore, the estimation procedure is robust against state preparation imperfections, and naturally yields the same precision for all values of the estimated phase. We implement the proposed scheme experimentally, using a polarisation interferometer probed by a single-photon signal, and temporally multiplexing a single homodyne detector. We repeat the experiment with classical probe states. For both cases, we demonstrate the accuracy and precision of the proposed method, our implementation deviating by 5% from the fundamental precision bound. We demonstrate that, in our scheme, single-photon probe states can provide better precision than weak coherent ones. These results indicate that hybrid quantum resources, which combine tools from the discrete and continuous-variable paradigms, can play a signi cant role in practical sensing scenarios. In the second part of this thesis, we present an application in the eld of information thermodynamics, reporting an experimental realisation, in a photonic setup, of Maxwell's demon. We show that a measurement at the few-photons level, followed by a feed-forward operation, allows the extraction of work from intense thermal light into an electric circuit. The interpretation of the experiment leads us to the derivation of an equality relating work extraction to information acquired by measurement. We prove a bound using this relation, and show that it is in agreement with the experimental results. Our work puts forward photonic systems as a platform for experiments in the eld of information thermodynamics. In the third part of this thesis, we present a new method for the characterisation of broadband parametric down-conversion, based on stimulated frequency generation. In particular, we analyse the information contained in the frequency generation produced in the same mode as a seeding beam, for a type-II down-conversion process. We derive a model for this signal and argue that its detection can provide a useful characterisation tool in the high-gain regime, allowing for a self-referenced estimation of squeezing gain. We propose a method for measuring this signal and present an experimental realisation, based on a wave-guided source, at telecommunication wavelengths. Our experimental results demonstrate that the proposed measurement is an e ective experimental handle for discerning the intricate structure of broadband parametric down-conversion.
The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.