Measurement and control of quantum systems play an important role in science and technology, from the foundations of quantum mechanics to practical applications. This thesis presents theoretical and experimental work that exploits quantum measurement and measurement-based feedback control to study some new problems in the contexts of solid state physics and optical quantum systems. In the first part, we consider the dynamics of open quantum systems conditioned on continuous measurements. We revisit the fact that dynamical quantum events are detector dependent by framing the problem as a quantum correlation test of the Einstein-Podolsky-Rosen (EPR) steering type. In this regards, a no-go theorem for quantum diusion is derived. In order to study a realistic experimental situation we scrutinise dierent physical systems, Einstein-Podolsky-Rosen steering inequalities and measurement protocol. We show that the no-go result for quantum diusion is not universal and does not apply to quantum jumps by devising a novel adaptive measurement scheme. Since the objectiveness of pure-state dynamical models is ruled out by quantum entanglement, then it is reasonable to say that quantum jumps are more quantum than quantum diusion. In the rst part we also study a stochastic feedback control of quantum transport. We show that using a feedback control strategy it is possible to restrict the dynamics of a double quantum dot system to a non-orthogonal two-state ensemble. The feedback control approach can be less experimentally challenging than an adaptive measurement scheme, as the latter requires implementing local oscillators, which might be dicult to realise in mesoscopic physics.
Measurement and control of quantum systems play an important role in science and technology, from the foundations of quantum mechanics to practical applications. This thesis presents theoretical and experimental work that exploits quantum measurement and measurement-based feedback control to study some new problems in the contexts of solid state physics and optical quantum systems. In the first part, we consider the dynamics of open quantum systems conditioned on continuous measurements. We revisit the fact that dynamical quantum events are detector dependent by framing the problem as a quantum correlation test of the Einstein-Podolsky-Rosen (EPR) steering type. In this regards, a no-go theorem for quantum diusion is derived. In order to study a realistic experimental situation we scrutinise dierent physical systems, Einstein-Podolsky-Rosen steering inequalities and measurement protocol. We show that the no-go result for quantum diusion is not universal and does not apply to quantum jumps by devising a novel adaptive measurement scheme. Since the objectiveness of pure-state dynamical models is ruled out by quantum entanglement, then it is reasonable to say that quantum jumps are more quantum than quantum diusion. In the rst part we also study a stochastic feedback control of quantum transport. We show that using a feedback control strategy it is possible to restrict the dynamics of a double quantum dot system to a non-orthogonal two-state ensemble. The feedback control approach can be less experimentally challenging than an adaptive measurement scheme, as the latter requires implementing local oscillators, which might be dicult to realise in mesoscopic physics.
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of open quantum systems lead to the theory of continuous measurement and quantum trajectories, in which wave function collapse occurs over a finite time scale associated with an interaction. Within this formalism, it becomes possible to ask many new questions that would be trivial or even ill-defined in the context of the more basic measurement model. In this thesis, we investigate both theoretically and experimentally what fundamentally new capabilities arise when an experimental apparatus can resolve the continuous dynamics of a measurement. Theoretically, we show that when one can perform feedback operations on the timescale of the measurement process, the resulting tools provide significantly more control over entanglement generation, and in some settings can generate it optimally. We derive these results using a novel formalism which encompasses most known quantum feedback protocols. Experimentally, we show that continuous measurement allows one to observe the dynamics of a system undergoing simultaneous non-commuting measurements, which provides a reinterpretation of the Heisenberg uncertainty principle. Finally, we combine the theoretical focus on quantum feedback with the experimental capabilities of superconducting circuits to implement a feedback controlled quantum amplifier. The resulting system is capable of adaptive measurement, which we use to perform the first canonical phase measurement.
Quantum systems exhibit unique behaviors governed by principles distinct from classical physics, notably in the realms of measurement and control. This paper explores the fundamental concepts and applications of quantum measurement and feedback control in quantum systems. Measurement in quantum mechanics disrupts the state of a system due to the inherent probabilistic nature of quantum states. This disruption, often described by the collapse of the wave function, presents challenges and opportunities for understanding and manipulating quantum states. Quantum measurement theory addresses how observations affect quantum states and the role of measurement devices in this process. Feedback control mechanisms offer a pathway to mitigate the disruptive effects of measurement and harness them for coherent quantum operations. By continuously monitoring and adjusting quantum systems based on measurement outcomes, feedback control enables stabilization, state preparation, and enhanced coherence times. Examples include quantum error correction, quantum state tomography, and real-time manipulation of quantum bits (qubits).
Tests of the predictions of quantum mechanics for entangled systems have provided increasing evidence against local realistic theories. However, there remains the crucial challenge of simultaneously closing all major loopholes—the locality, freedom-of-choice and detection loopholes—in a single experiment. An important sub-class of local realistic theories can be tested with the concept of 'steering'. The term 'steering' was introduced by Schrödinger in 1935 for the fact that entanglement would seem to allow an experimenter to remotely steer the state of a distant system as in the Einstein–Podolsky–Rosen (EPR) argument. Einstein called this 'spooky action at a distance'. EPR-steering has recently been rigorously formulated as a quantum information task opening it up to new experimental tests. Here, we present the first loophole-free demonstration of EPR-steering by violating three-setting quadratic steering inequality, tested with polarization-entangled photons shared between two distant laboratories. Our experiment demonstrates this effect while simultaneously closing all loopholes: both the locality loophole and a specific form of the freedom-of-choice loophole are closed by having a large separation of the parties and using fast quantum random number generators, and the fair-sampling loophole is closed by having high overall detection efficiency. Thereby, we exclude—for the first time loophole-free—an important class of local realistic theories considered by EPR. Besides its foundational importance, loophole-free steering also allows the distribution of quantum entanglement secure event in the presence of an untrusted party.
Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.
Einstein-Podolsky-Rosen (EPR) steering, a generalization of the original concept of "steering" proposed by Schrödinger, describes the ability of one system to nonlocally affect another system's states through local measurements. Some experimental efforts to test EPR steering in terms of inequalities have been made, which usually require many measurement settings. Analogy to the "all-versus-nothing" (AVN) proof of Bell's theorem without inequalities, testing steerability without inequalities would be more strong and require less resources. Moreover, the practical meaning of steering implies that it should also be possible to store the state information on the side to be steered, a result that has not yet been experimentally demonstrated. Using a recent AVN criterion for two-qubit entangled states, we experimentally implement a practical steering game using quantum memory. Furthermore, we develop a theoretical method to deal with the noise and finite measurement statistics within the AVN framework and apply it to analyze the experimental data. Our results clearly show the facilitation of the AVN criterion for testing steerability and provide a particularly strong perspective for understanding EPR steering.
Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.