In this letter, we study the resource allocation for a multiuser intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) system. Specifically, a multi-antenna base station (BS) transmits energy and info
rmation signals simultaneously to multiple energy harvesting receivers (EHRs) and information decoding receivers (IDRs) assisted by an IRS. Under this setup, we introduce a multi-objective optimization (MOOP) framework to investigate the fundamental trade-off between the data sum-rate maximization and the total harvested energy maximization, by jointly optimizing the energy/information beamforming vectors at the BS and the phase shifts at the IRS. This MOOP problem is first converted to a single-objective optimization problem (SOOP) via the $epsilon$-constraint method and then solved by majorization minimization (MM) and inner approximation (IA) techniques. Simulation results unveil a non-trivial trade-off between the considered competing objectives, as well as the superior performance of the proposed scheme as compared to various baseline schemes.
State-of-the-art sensors of force, motion and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached the Standar
d Quantum Limit (SQL), which directly follows from the Heisenberg uncertainty relation and corresponds to balancing the measurement imprecision and the perturbation of the probe by the quantum back action of the meter. The SQL is not truly fundamental and several methods for its overcoming have been proposed and demonstrated. At the same time, two quantum sensitivity constraints which are more fundamental are known. The first limit arises from the finiteness of the probing strength (in the case of optical interferometers - of the circulating optical power) and is known as the Energetic Quantum Limit or, in a more general context, as the Quantum Cram{e}r-Rao Bound (QCRB). The second limit arises from the dissipative dynamics of the probe, which prevents full efficacy of the quantum back action evasion techniques developed for overcoming the SQL. No particular name has been assigned to this limit; we propose the term Dissipative Quantum Limit (DQL) for it. Here we develop a unified theory of these two fundamental limits by deriving the general sensitivity constraint from which they follow as particular cases. Our analysis reveals a phase transition occurring at the boundary between the QCRB-dominated and the DQL regimes, manifested by the discontinuous derivatives of the optimal spectral densities of the meter field quantum noise. This leads to the counter-intuitive (but favorable) finding that quantum-limited sensitivity can be achieved with certain lossy meter systems. Finally, we show that the DQL originates from the non-autocommutativity of the internal thermal noise of the probe and that it can be overcome in non-stationary measurements.
Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to consider
ably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or the noise is high. Here, we experimentally demonstrate a remedy against loss and noise: strong noiseless amplification before detection. This way, we achieve loss-tolerant operation of an interferometer fed with squeezed and coherent light. With only 50% detection efficiency and with noise exceeding the level of squeezed light more than 50 times, we overcome the shot-noise limit by 6~dB. Sub-shot-noise phase sensitivity survives up to 87% loss. Application of this technique to other types of optical sensing and imaging promises a full use of quantum resources in these fields.
Gravitational wave detectors (GWDs), which have brought about a new era in astronomy, have reached such a level of maturity that further improvement necessitates quantum-noise-evading techniques. Numerous proposals to this end have been discussed in
the literature, e.g., invoking frequency-dependent squeezing or replacing the current Michelson interferometer topology by that of the quantum speedmeter. Recently, a proposal based on the linking of a standard interferometer to a negative-mass spin system via entangled light has offered an unintrusive and small-scale new approach to quantum noise evasion in GWDs [Phys. Rev. Lett. $mathbf{121}$, 031101 (2018)]. The solution proposed therein does not require modifications to the highly refined core optics of the present GWD design and, when compared to previous proposals, is less prone to losses and imperfections of the interferometer. In the present article, we refine this scheme to an extent that the requirements on the auxiliary spin system are feasible with state-of-the-art implementations. This is accomplished by matching the effective (rather than intrinsic) susceptibilities of the interferometer and spin system using the virtual rigidity concept, which, in terms of implementation, requires only suitable choices of the various homodyne, probe, and squeezing phases.
Quantum fluctuation of light limits the sensitivity of advanced laser interferometric gravitational-wave detectors. It is one of the principal obstacles on the way towards the next-generation gravitational-wave observatories. The envisioned significa
nt improvement of the detector sensitivity requires using quantum non-demolition measurement and back-action evasion techniques, which allow us to circumvent the sensitivity limit imposed by the Heisenberg uncertainty principle. In our previous review article: Quantum measurement theory in gravitational-wave detectors [Living Rev. Relativity 15, 5 (2012)], we laid down the basic principles of quantum measurement theory and provided the framework for analysing the quantum noise of interferometers. The scope of this paper is to review novel techniques for quantum noise suppression proposed in the recent years and put them in the same framework. Our delineation of interferometry schemes and topologies is intended as an aid in the process of selecting the design for the next-generation gravitational-wave observatories.
Measurement-induced back action, a direct consequence of the Heisenberg Uncertainty Principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Let
t. {bf 108}, 033602 (2012)], and show that results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise --- through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the Standard Quantum Limit.
The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour of such immense measurement devices as kil
ometer-long interferometers starts to matter. The time, when their sensitivity will be mainly limited by the quantum noise of light is round the corner, and finding the ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of Standard Quantum Limit and the methods of its surmounting.
Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit, a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Un
certainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the Standard Quantum Limit significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.
We develop here algorithms which allow to find regimes of signal-recycled Fabry-Perot--Michelson interferometer (for example, Advanced LIGO), optimized concurrently for two (binary inspirals + bursts) and three (binary inspirals + bursts + millisecon
d pulsars) types of gravitational waves sources. We show that there exists a relatevely large area in the interferometer parameters space where the detector sensitivity to the first two kinds of sources differs only by a few percent from the maximal ones for each kind of source. In particular, there exists a specific regime where this difference is ~0.5 for both of them. Furthermore we show that even more multipurpose regimes are also possible, that provide significant sensitivity gain for millisecond pulsars with only minor sensitivity degradation for binary inspirals and bursts.
