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By J. Batle-Vallespir

The current Thesis covers the topic of the characterization of entangled states by means of recourse to entropic measures, in addition to the outline of entanglement with regards to a number of matters in quantum mechanics, resembling the rate of a quantum evolution or the connections latest among quantum entanglement and quantum section transitions.

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Extra resources for Characterization of Quantum Entangled States [thesis]

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Wehrl. See Ref. [52] 27 the event horizon, exactly 1/4 of it as measured in Planck units30 . So to speak, one bit of information is encoded in four Planck areas. But as the black hole evaporates, its mass decreases, as well as its surface. The generalization of the Second Law could find an explanation to this paradox: the entropy of the outgoing radiation compensates the loss of information of the black hole. However one must be careful with entropies. The Shannon entropy and the thermodynamical entropy are conceptually equivalent: the number of configurations that are counted in the Boltzmann-Gibbs entropy shows the quantity of Shannon information that would be needed to carry out any given configuration.

However, in the foreseeable future, each element would shrink to a size at which quantum effects become important. Arrived at this point, there exist two possibilities: i) to get stuck to the usual Boolean algebra of 0’s and 1’s, though employing ultimate quantum devices such as single electron transistors, or ii) to take advantage of these quantum effects in order to perform a new conception of computation, a quantum computation. Clearly the first option represents a short-term answer to speeding up computations, but a quantum computer –if ever built– will definitely constitute a long-term solution.

Quite recently [49], there have been claims that affirm that there is a fundamental limit to how long quantum coherence can last, showing that spontaneous fluctuations can destroy quantum coherence in a time period that depends on the size and temperature of the system. Luckily, proposals for quantum computation tend to invoke bits at smaller scales, so they are not undermined. The Schr¨odinger cat is points out the paradoxes of playing quantum games with macroscopic objects (probably our intuition crashes more with the cat being in a superposition of dead and alive, which is obviously a property of animated beings, rather than considering it as a macroscopic object).

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Characterization of Quantum Entangled States [thesis] by J. Batle-Vallespir


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