5,517 research outputs found
Information In The Non-Stationary Case
Information estimates such as the ``direct method'' of Strong et al. (1998)
sidestep the difficult problem of estimating the joint distribution of response
and stimulus by instead estimating the difference between the marginal and
conditional entropies of the response. While this is an effective estimation
strategy, it tempts the practitioner to ignore the role of the stimulus and the
meaning of mutual information. We show here that, as the number of trials
increases indefinitely, the direct (or ``plug-in'') estimate of marginal
entropy converges (with probability 1) to the entropy of the time-averaged
conditional distribution of the response, and the direct estimate of the
conditional entropy converges to the time-averaged entropy of the conditional
distribution of the response. Under joint stationarity and ergodicity of the
response and stimulus, the difference of these quantities converges to the
mutual information. When the stimulus is deterministic or non-stationary the
direct estimate of information no longer estimates mutual information, which is
no longer meaningful, but it remains a measure of variability of the response
distribution across time
Efficient one-step generation of large cluster states with solid-state circuits
Highly entangled states called cluster states are a universal resource for
measurement-based quantum computing (QC). Here we propose an efficient method
for producing large cluster states using superconducting quantum circuits. We
show that a large cluster state can be efficiently generated in just one step
by turning on the inter-qubit coupling for a short time. Because the
inter-qubit coupling is only switched on during the time interval for
generating the cluster state, our approach is also convenient for preparing the
initial state for each qubit and for implementing one-way QC via single-qubit
measurements. Moreover, the cluster state is robust against parameter
variations.Comment: 4 pages, 1 figur
The Friedmann equation in modified entropy-area relation from entropy force
According to the formal holographic principle, a modification to the
assumption of holographic principle in Verlinder's investigation of entropy
force is obtained. A more precise relation between entropy and area in the
holographic system is proposed. With the entropy corrections to the
area-relation, we derivate Newton's laws and Einstein equation with a static
spherically symmetric holographic screen. Furthermore we derived the correction
terms to the modified Friedmann equation of the FRW universe starting from the
holographic principle and the Debye model.Comment: Mod. Phys. Lett. A26, 489-500 (2011
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