The existence of ideal quantum measurements is one of the fundamental predictions of quantum mechanics. In theory, an ideal measurement projects a quantum state onto the eigenbasis of the measurement observable, while preserving coherences between eigenstates that have the same eigenvalue. The question arises whether there are processes in nature that correspond to such ideal quantum measurements and how such processes are dynamically implemented in nature. Here we address this question and present experimental results monitoring the dynamics of a naturally occurring measurement process: the coupling of a trapped ion qutrit to the photon environment. By taking tomographic snapshots during the detection process, we show that the process develops in agreement with the model of an ideal quantum measurement with an average fidelity of 94%.
The existence of ideal quantum measurements is one of the fundamental predictions of quantum mechanics. In theory, an ideal measurement projects a quantum state onto the eigenbasis of the measurement observable, while preserving coherences between eigenstates that have the same eigenvalue. The question arises whether there are processes in nature that correspond to such ideal quantum measurements and how such processes are dynamically implemented in nature. Here we address this question and present experimental results monitoring the dynamics of a naturally occurring measurement process: the coupling of a trapped ion qutrit to the photon environment. By taking tomographic snapshots during the detection process, we show that the process develops in agreement with the model of an ideal quantum measurement with an average fidelity of 94%.
Abstract When a quantum state is subjected to a measurement and the state is not an eigenstate of the dynamical variable being measured, the outcome is unpredictable. Only the probabilities of the various possible outcomes are predicted by theory. This phenomenon is sometimes discussed in terms of “wavefunction collapse.” Trapped ions can be used for real, as opposed to gedanken demonstrations of this basic process. In the experiments described here, a single ion, or a few identical ions, were prepared in well defined superpositions of two internal energy eigenstates. The populations of the energy levels were then measured. When the state amplitudes were equal, the population fluctuations were greater than when one of the amplitudes was nearly zero, in agreement with the predictions of quantum mechanics. In other experiments, such as those with atomic beams, the number of atoms under observation fluctuates, and this obscures the fluctuations from other sources. However, if the number of atoms is small and constant, the fundamental quantum mechanical fluctuations can be observed.
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.
The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system interacting with the measuring device and show under which ideal conditions the measure process may ideally work. Our procedure leads to the conclusion that there is no hope that any experimental procedure will be able to lead to a clean solution of the process, except maybe in very specific cases. The reasons for this situation are deeply rooted in the fundamental properties of quantum theory.
The subject–object distinction is indeed at the very root of the unease that many people still feel in connection with quantum mechanics. Some such distinction is dictated by the postulates of the theory, but exactly where or when to make it is not prescribed. Thus in the classic treatise of Dirac we learn the fundamental propositions: … any result of a measurement of a real dynamical variable is one of its eigenvalues …, … if the measurement of the observable ξ for the system in the state corresponding to | x 〈 is made a large number of times, the average of all the results obtained will be 〈 x |ξ| x 〉 …, … a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured …. So the theory is fundamentally about the results of ‘measurements’, and therefore presupposes in addition to the ‘system’ (or object) a ‘measurer’ (or subject). Now must this subject include a person? Or was there already some such subject–object distinction before the appearance of life in the universe? Were some of the natural processes then occurring, or occurring now in distant places, to be identified as ‘measurements’ and subjected to jumps rather than to the Schrödinger equation? Is ‘measurement’ something that occurs all at once? Are the jumps instantaneous? And so on.
An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability. Preparatory measurements are measurements for which we can con- clude on the basis of the result of measurement that the system is (immediately after measurement) in an eigenstate of the eigenvalue corresponding to the given result. Preparatory measurements are first of all experimental processes that select an ensemble to which a quantum (statistical) state can be assigned. Statistical interpretations of the state vector take as fundamental this assignment of a quantum state to (sub)ensembles selected by experimental procedures. But if the exist- ence of hidden variables is denied, then it seems that it should be possible to interpret preparatory measurements in terms of individual state transformations. This can be done by thinking of these measure- ments as idealized measurement transformations satisfying the so-called first kind condition: an immediate repetition of the same measurement gives the same result as the initial measurement. This idealization (taken here for the sake of simplicity) will be assumed here to be non-controversial. Furthermore, it will be assumed here that every measurement can be represented as a first kind measurement: thus, a 'measurement' in this investigation is always to be a 'first kind measure- ment'. For measurements of maximal magnitudes (i.e., magnitudes with no degenerate eigenvalue) Von Neumann argued (1955) that the final state is given by the (unique) eigenstate of the eigenvalue representing the