A quantum measurement process, when non-trivial, is not a closed evolution: the appearance of classical outcomes is usually interpreted as the evidence of some decoherence-like mechanism causing quantum superpositions to degrade into classical mixtures. Such mechanism is due to a net flow of information from the input system (measurement object), through the physical apparatus interacting with the object (measurement probe), into some environment, the latter representing all those degrees of freedom which are not directly accessible by the experimenter. For this reason, the phenomenon of state reduction induced by the measurement process generally entails an irreversible state change. The aim of our contribution is to answer the following questions : how much information a measurement is able to extract? "How much" irreversible is the state reduction due to a particular measurement process? In which way information gain and irreversibility are related?
A quantum measurement process, when non-trivial, is not a closed evolution: the appearance of classical outcomes is usually interpreted as the evidence of some decoherence-like mechanism causing quantum superpositions to degrade into classical mixtures. Such mechanism is due to a net flow of information from the input system (measurement object), through the physical apparatus interacting with the object (measurement probe), into some environment, the latter representing all those degrees of freedom which are not directly accessible by the experimenter. For this reason, the phenomenon of state reduction induced by the measurement process generally entails an irreversible state change. The aim of our contribution is to answer the following questions : how much information a measurement is able to extract? "How much" irreversible is the state reduction due to a particular measurement process? In which way information gain and irreversibility are related?
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.
Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the principal constraints of quantum-mechanical origin, the information about the purity of S state isn't transferred to O during the measurement of arbitraryS observable V. Consequently O can't discriminate the pure and mixed S ensembles with the same . As the result, the random outcomes should be detected by O in V measurement for S pure ensemble of V eigenstate superposition. It's shown that the outcome probabilties obey to Born rule. The influence of O decoherence by its environment is studied, however the account of its effects doesn't change these results principally.
The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus; (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the 'collapse of the wave function') is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e. whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions (1) and (2) to hold when and only when information about measurement results persists. Finally the notion of 'element of reality' introduced by Einstein, Podolsky and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the 'classical' nature of the world we experience.
The two main types of quantum measurements von Neumann's postulate of the reduction of the wave function answers the question of what happens to the quantum object during the measurement. However, the reduction postulate does not answer the question of how the measuring device must be designed to realize the desired measurement. To answer this second question, one must understand the connection between the measuring device as an ordinary physical system, and the nature of the desired measurement (the quantity to be measured, the desired precision, and the choice of how the measurement is to perturb the quantum object). The Schrödinger equation cannot tell us the connection between the design of the measuring device and the nature of the measurement, because the Schrödinger equation neither governs nor describes the process of measurement. More specifically: The evolution of the wave function as described by the Schrödinger equation has two key features: it is a reversible evolution (from the final state in principle one can always evolve back to the initial one), and it is a deterministic evolution (the final state is determined uniquely by the initial one). By contrast, the reduction of the wave function in a measurement is irreversible (once the measurement is finished and the information has been extracted from it, it is impossible to return to the pre-measurement state), and it is nondeterministic (one cannot predict, before the measurement, the post-measurement state of the measured object).
We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about a particular system. The measurement apparatus is assumed to contain a large number of degrees of freedom, and the measurement outcomes are obtained by looking at the long interaction time limit. We study two cases which show contrasting behaviour. With a fixed axis coupling, the measurement is performed along the pointer basis with a high degree of robustness, for a wide variety of bath states. In a second model with Heisenberg interactions, the measurement outcomes can be altered considerably by changing the state of the bath.