Quantum tomography (original) (raw)
Die Quantentomographie ist ein Verfahren zur Rekonstruktion eines Quantenzustandes aus einer Reihe von Messungen. Sie ermöglicht die vollständige Vermessung des Quantenzustandes eines Objektes, z. B. seine Dichtematrix oder seine Ort- und Impulsverteilung. Da aufgrund der Unschärferelation die Messung den Quantenzustand verändert, rekonstruiert die Quantentomographie den wahrscheinlichen Zustand vor der Messung. * Das Prinzip * 1. Ein Zustand * 2. Viele Messungen an Zustandskopien * 3. Rekonstruktion des Gesamtzustandes vor der Messung
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| dbo:abstract | Die Quantentomographie ist ein Verfahren zur Rekonstruktion eines Quantenzustandes aus einer Reihe von Messungen. Sie ermöglicht die vollständige Vermessung des Quantenzustandes eines Objektes, z. B. seine Dichtematrix oder seine Ort- und Impulsverteilung. Um den Zustand eindeutig identifizieren zu können, müssen die Messungen tomographisch vollständig sein. Nur wenn man genügend Messungen an Zustandskopien vornimmt, kann man den gesamten Zustandsvektor rekonstruieren. Auf diese Weise wird die Wigner-Funktion zur Darstellung eines Quantenzustandes bestimmt, deren Projektionen experimentell zugänglich sind. Da aufgrund der Unschärferelation die Messung den Quantenzustand verändert, rekonstruiert die Quantentomographie den wahrscheinlichen Zustand vor der Messung. * Das Prinzip * 1. Ein Zustand * 2. Viele Messungen an Zustandskopien * 3. Rekonstruktion des Gesamtzustandes vor der Messung (de) Quantum tomography or quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states. The source of these states may be any device or system which prepares quantum states either consistently into quantum pure states or otherwise into general mixed states. To be able to uniquely identify the state, the measurements must be tomographically complete. That is, the measured operators must form an operator basis on the Hilbert space of the system, providing all the information about the state. Such a set of observations is sometimes called a quorum. In quantum process tomography on the other hand, known quantum states are used to probe a quantum process to find out how the process can be described. Similarly, quantum measurement tomography works to find out what measurement is being performed. Whereas, randomized benchmarking scalably obtains a figure of merit of the overlap between the error prone physical quantum process and its ideal counterpart. The general principle behind quantum state tomography is that by repeatedly performing many different measurements on quantum systems described by identical density matrices, frequency counts can be used to infer probabilities, and these probabilities are combined with Born's rule to determine a density matrix which fits the best with the observations. This can be easily understood by making a classical analogy. Consider a harmonic oscillator (e.g. a pendulum). The position and momentum of the oscillator at any given point can be measured and therefore the motion can be completely described by the phase space. This is shown in figure 1. By performing this measurement for a large number of identical oscillators we get a probability distribution in the phase space (figure 2). This distribution can be normalized (the oscillator at a given time has to be somewhere) and the distribution must be non-negative. So we have retrieved a function W(x,p) which gives a description of the chance of finding the particle at a given point with a given momentum. For quantum mechanical particles the same can be done. The only difference is that the Heisenberg's uncertainty principle mustn't be violated, meaning that we cannot measure the particle's momentum and position at the same time. The particle's momentum and its position are called quadratures (see Optical phase space for more information) in quantum related states. By measuring one of the quadratures of a large number of identical quantum states will give us a probability density corresponding to that particular quadrature. This is called the marginal distribution, pr(X) or pr(P) (see figure 3). In the following text we will see that this probability density is needed to characterize the particle's quantum state, which is the whole point of quantum tomography. (en) Квантовая томография — часть квантовой информатики. Квантовая томография занимается восстановлением амплитуд квантового состояния по результатам его многократных измерений, и нахождением оптимальных схем таких измерений. Если — набор комплексных чисел, сумма квадратов модулей которых равна 1, то по ним однозначно можно построить квантовое состояние вида Томография решает обратную задачу: по данному состоянию восстановить всё . Для этого необходимо производить измерение состояния в разных базисах, то есть для каждого нового измерения необходимо иметь новое, свежеприготовленное состояние . Имея только один экземпляр состояния , нельзя определить его амплитуды со сколько-нибудь приемлемой точностью. Это следует из оценки на объём классической информации, которую можно извлечь из квантового состояния, а также из следующей теоремы. (ru) |
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| rdfs:comment | Die Quantentomographie ist ein Verfahren zur Rekonstruktion eines Quantenzustandes aus einer Reihe von Messungen. Sie ermöglicht die vollständige Vermessung des Quantenzustandes eines Objektes, z. B. seine Dichtematrix oder seine Ort- und Impulsverteilung. Da aufgrund der Unschärferelation die Messung den Quantenzustand verändert, rekonstruiert die Quantentomographie den wahrscheinlichen Zustand vor der Messung. * Das Prinzip * 1. Ein Zustand * 2. Viele Messungen an Zustandskopien * 3. Rekonstruktion des Gesamtzustandes vor der Messung (de) Quantum tomography or quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states. The source of these states may be any device or system which prepares quantum states either consistently into quantum pure states or otherwise into general mixed states. To be able to uniquely identify the state, the measurements must be tomographically complete. That is, the measured operators must form an operator basis on the Hilbert space of the system, providing all the information about the state. Such a set of observations is sometimes called a quorum. (en) Квантовая томография — часть квантовой информатики. Квантовая томография занимается восстановлением амплитуд квантового состояния по результатам его многократных измерений, и нахождением оптимальных схем таких измерений. Если — набор комплексных чисел, сумма квадратов модулей которых равна 1, то по ним однозначно можно построить квантовое состояние вида (ru) |
| rdfs:label | Quantentomographie (de) Quantum tomography (en) Квантовая томография (ru) |
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