We examine stochastic maps in the context of quantum optics. Making use of the master equation, the damping basis, and the Bloch picture we calculate a non-unital, completely positive, trace-preserving map with unequal damping eigenvalues. This results in what we call the squeezed vacuum channel. A geometrical picture of the effect of stochastic noise on the set of pure state qubit density operators is provided. Finally, we study the capacity of the squeezed vacuum channel to transmit quantum information and to distribute EPR states.
We examine the quantum states produced through parametric amplification with internal quantum noise. The internal diffusion arises by coupling both modes of light to a reservoir for the duration of the interaction time. The Wigner function for the diffused two-mode squeezed state is calculated. The nonlocality, separability, and purity of these quantum states of light are discussed. In addition, we conclude by studying the nonlocality of two other continuous variable states: the Werner state and the phase-diffused state for two light modes.
We present a scheme that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. The state is near optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes a Gaussian entanglement distillation protocol and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter. Bell's theorem is regarded by some as one of the most profound discoveries of science in the 20th century. Not only does it provide a quantifiable measure of correlations stronger than any allowed classically, which is a key resource in many quantum-information processing applications, it also addresses fundamental questions in the foundations of quantum mechanics. In 1964, Bell quantified Bohm's version of the Einstein-Podolsky-Rosen ͑EPR͒ gedanken experiment by introducing an inequality that provides a test of local hidden variable ͑LHV͒ models ͓1͔. A violation of Bell's inequality forces one to conclude that, contrary to the view held by EPR, quantum mechanics cannot be both local and real. In order to experimentally support this conclusion in a strict sense, a Bell test that is free from loopholes is required. Although it is still quite remarkable that such seemingly metaphysical questions can even be put to the test in the laboratory, a loophole-free Bell test has yet to be achieved.For more than three decades, numerous experiments have confirmed the predictions of the quantum theory, thereby disproving local realistic models as providing a correct description of physical reality ͓2͔. However, all experiments performed to date suffer from at least one of the two primary loopholes: the detection loophole and the locality loophole. The detection loophole arises due to low detector efficiencies that may not permit an adequate sampling of the ensemble space while the locality loophole suggests that component parts of the experimental apparatus that are not spacelike separated could influence each other. The majority of Bell tests have used optical systems to measure correlations, some achieving spacelike separations but still subjected to lowefficiency photodetectors ͑see, e.g., Ref. ͓3͔͒. Correlations in the properties of entangled ions were shown to violate a Bell inequality using high-efficiency detectors, eliminating the detection loophole; however, the ions were not spacelike separated ͓4͔. A major challenge that has yet to be achieved is to experimentally realize a single Bell test that closes these loopholes.The ease with which optical setups address the locality loophole coupled with the currently achievable high efficiencies ͑Ͼ0.95͒ of homodyne detectors makes Bell tests using quadrature-phase measurements good candidates for a loophole-free experiment. Furthermore, continuous quadrature amplitudes are the optical analog of position and momentum and more closely resemble the original state considered by EP...
The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.
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