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dagrep_v005_i004_p123_s15181. - DROPS
dagrep_v005_i004_p123_s15181. - DROPS

... pGCL. Besides the usual language constructs in Dijkstra’s GCL such as non-deterministic choice, it features a probabilistic choice where the probability distribution may be parametric. For instance, the assignment x += 1 [p] skip increments the variable x by one with probability p, and keeps the val ...
Full text in PDF form
Full text in PDF form

... not attempt to define an information content of a physical system as a whole, but rather we wish to set appropriate measures of uncertainty and information for concrete pure states of a quantum system. A particular quantum state should not be misinterpreted to provide a complete description of the c ...
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... For thermal chaotic light with Guassian PE1, E2  we get that P ( ) depends exclusively on the standard second order degree of coherence |  | . Moreover,  approximately coincides with |  | as shown in the next figure. ...
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... orthogonal states, only one of those states can be observed, or measured. After measurement, the system is no longer in superposition: the quantum state collapses into the one state measured, and the probability amplitude of all other states goes to is measured, zero. For example, when the state the ...
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De finetti theorems, mean-field limits and bose

Quantum structures, separated physical entities and probability
Quantum structures, separated physical entities and probability

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... all the members have sharply defined values for the canonically conjugate variables. This minimal interpretation states that it is not possible to prepare pure ensembles in which all systems have the same values for these quantities, or ensembles in which the spreads are smaller than allowed by quan ...
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... applications, such as quantum computation [2, 3] and quantum metrology [6]. The phenomenon of decoherence comprises, basically, a family of effects arising from the interaction (and the accompanying entanglement-development) between quantum systems and their environments [3, 4]. Physical systems in ...
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... or quantum dashes [6]–[8]. The latter have been shown to behave as a self-assembly quantum wires (SAQWRs) [9]. All such nanostructure gain media comprise a reservoir through which carriers are fed to the gain region via complex carrier relaxation mechanisms [10]. There is a finite steady-state carri ...
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... Alice encodes a random bit into a qubit in one of two bases, either X or Z, chosen at random. The X bits will be used to extract a key, while the Z are used to check security. She sends the qubit over a public channel to Bob, while the eavesdropper, Eve, may interfere as she wishes. Bob measures the ...
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... quantized Hall effect [4—7],by contrast, contradicts the one-particle picture. The one-particle picture would lead one to expect a vast sea of degenerate or nearly degenerate states, with no gap, when the valence Landau band is partially filled. Thus non-trivial correlations among the electrons must ...
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... Our study of the entanglement properties of correlated wave functions for spin lattices was motivated by the work of Osterloh et al. [26] and more especially that of Osborne and Nielsen (ON) [27]. These authors were the rst to explore possible connections between quantum phase transitions and entan ...
Qualitative individuation in permutation
Qualitative individuation in permutation

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Probability amplitude



In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.
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