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Quantum tomography or quantum state tomography is the process of reconstructing the quantum state (density matrix) for a source of quantum systems by measurements on the systems coming from the source.〔Quantum State Tomography. http://research.physics.uiuc.edu/QI/Photonics/Tomography/#what_is_tomography〕 The source 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. 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. Let us 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 possibility 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. == What quantum state tomography is used for == Quantum tomography is applied on a source of systems, to determine what the quantum state is of the output of that source. Unlike a measurement on a single system, which determines the system's current state after the measurement (in general, the act of making a measurement alters the quantum state), quantum tomography works to determine the state(s) prior to the measurements. Quantum tomography can be used for characterizing optical signals, including measuring the signal gain and loss of optical devices,〔G. Mauro D’Ariano et al. Quantum tomography as a tool for the characterization of optical devices. http://www.iop.org/EJ/abstract/1464-4266/4/3/366〕 as well as in quantum computing and quantum information theory to reliably determine the actual states of the qubits.〔Robin Blume-Kohout. Optimal, reliable estimation of quantum states. http://arxiv.org/abs/quant-ph/0611080v1〕〔A.I.Lvovsky, M.G.Raymer. Continuous-variable optical quantum state tomography. http://arxiv.org/abs/quant-ph/0511044v2〕 One can imagine a situation in which a person Bob prepares some quantum states and then gives the states to Alice to look at. Not confident with Bob's description of the states, Alice may wish to do quantum tomography to classify the states herself. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantum tomography」の詳細全文を読む スポンサード リンク
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