Quantum non-demolition measurements play an important role in quantum theory and many of its applications. In theory they are the most fundamental quantum measurements, but in practice their realization can be chal- lenging due to realistic constraints. In optics for example, most measurements are destructive since photons get absorbed by the detector. While some simple single particle non-demolition measurements are routinely done in optical setups by using a second degree of freedom to encode the results at an intermediate stage, measurements of degenerate non-local observables involving multiple photons remain challenging, especially when these are done at intermediate measurement strengths. Here we present an optical setup for performing variable strength non-demolition measurements of non-local observables in a pre and postselected setting. At the heart of the setup is an apparatus that can be used to turn a strong (projective) measurement into an arbitrary strength measurement by using a quantum eraser. We present our initial calibration results for this apparatus.
Quantum non-demolition measurements play an important role in quantum theory and many of its applications. In theory they are the most fundamental quantum measurements, but in practice their realization can be chal- lenging due to realistic constraints. In optics for example, most measurements are destructive since photons get absorbed by the detector. While some simple single particle non-demolition measurements are routinely done in optical setups by using a second degree of freedom to encode the results at an intermediate stage, measurements of degenerate non-local observables involving multiple photons remain challenging, especially when these are done at intermediate measurement strengths. Here we present an optical setup for performing variable strength non-demolition measurements of non-local observables in a pre and postselected setting. At the heart of the setup is an apparatus that can be used to turn a strong (projective) measurement into an arbitrary strength measurement by using a quantum eraser. We present our initial calibration results for this apparatus.
Nonlocal observables play an important role in quantum theory, from Bell inequalities and various postselection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a nonlocal scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for nonlocal observables without the need to communicate and adapt. The protocol can be used to perform weak and strong (projective) measurements, as well as measurements at any intermediate strength. It can also be used in practical situations beyond nonlocal measurements. We show how the protocol can be used to probe a version of Hardy's paradox with both weak and strong measurements. The outcomes of these measurements provide a nonintuitive picture of the pre- and postselected system. Our results shed new light on the interplay between quantum measurements, uncertainty, nonlocality, causality, and determinism.
This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.
In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.
Abstract In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.
According to Heisenberg’s uncertainty principle, measurement of a quantum observable introduces noise to this observable and thus limits the available precision of measurement. Quantum non-demolition measurements are designed to circumvent this limitation and have been demonstrated in detecting the photon flux of classical light beam. Quantum non-demolition measurement of a single photon is the ultimate goal because it is of great interest in fundamental physics and also a powerful tool for applications in quantum information processing. This chapter presents a brief introduction of the history and a review of the progress in quantum non-demolition measurement of light. In particular, a detailed description is presented for two works toward cavity-free schemes of quantum non-demolition measurement of single photons. Afterward, an outlook of the future in this direction is given.
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The act of measuring an observable of a quantum system introduces backaction noise to the measured system. In the most extreme case, the system gets destroyed with its state left unavailable for future measurement. An example is the photodetection process where photons are destroyed upon detection. It is desirable to consider schemes that avoid the back action effect induced on detected observable due to the measurement. Such measurement scheme in which one is able to repeat a measurement on a physical observable, with the result of each measurement being the same for all measurement times is known as quantum non-demolition (QND) measurement. With the QND measurement idea, it has become possible to detect photons without destroying its state. In this thesis, we present an optical QND measurement scheme known as the Mode invisibility technique to measure