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In [[quantum information]] theory, the '''Wehrl entropy''',<ref>{{cite doi|10.1103/RevModPhys.50.221|noedit}}</ref> named after A. Wehrl, is a type of quasi-[[entropy]] defined for the [[Husimi Q representation]] ''Q''(''x'',''p'') <ref>Kôdi Husimi (1940). "Some Formal Properties of the Density Matrix", ''Proc. Phys. Math. Soc. Jpn.'' '''22''': 264–314 .</ref>  of the phase-space [[quasiprobability distribution]]It is defined as
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:<math>S_Q = -\int Q(x,p) \log Q(x,p) \, dx \, dp ~.</math>
 
Such a definition of entropy relies on the fact that the Husimi Q representation remains non-negative definite,<ref>{{cite doi|10.1016/0378-4371(76)90145-X|noedit}}</ref> unlike other representations of quantum quasiprobability distributions in phase space.
 
However, it is not the fully quantum [[von Neumann entropy]] in the Husimi representation in phase space, {{math|− ∫ ''Q''<small></small> log<sub>★</sub>''Q'' &nbsp;''dx''&nbsp;''dp''}}:   all the requisite  star-products <small>★</small> in that entropy have been dropped here. In the Husimi representation, the star products read
:<math>  \star \equiv    \exp\left( \frac{\hbar}{2}
({\stackrel{\leftarrow}{\partial}}_x -i {\stackrel{\leftarrow}{\partial}}_p) ({\stackrel{\rightarrow}{\partial}}_x + i{\stackrel{\rightarrow}{\partial}}_p )  \right)~,</math>
and are isomorphic<ref>[[Cosmas Zachos|C. Zachos]], D. Fairlie, and [[Thomas Curtright|T. Curtright]], “Quantum Mechanics in Phase Space” (''World Scientific'', Singapore, 2005) ISBN 978-981-238-384-6 .</ref> to the [[Moyal product]]s of the [[Weyl quantization|Wigner–Weyl representation]].  
 
The Wehrl entropy, then, may be thought of as a type of heuristic semiclassical approximation to the full quantum von Neumann entropy, since it retains some ħ dependence, through ''Q'', but not all of it.
 
Like all entropies, it reflects some measure of non-localization,<ref>
{{cite journal
| last = Gnutzmann
| first = Sven
| coauthors = [[Karol Życzkowski|Karol Zyczkowski]]
| title = Rényi–Wehrl entropies as measures of localization in phase space
| journal = J. Phys. A: Math. Gen.
| volume = 34
| issue = 47
| year = 2001
| doi = 10.1088/0305-4470/34/47/317|arxiv = quant-ph/0106016 |bibcode = 2001JPhA...3410123G }}
</ref> as the [[Weierstrass transform|Gauss transform]] involved in generating ''Q'' and the sacrifice of the star operators have effectively discarded information. In general,
the Wehrl entropy exceeds the von Neumann entropy (which vanishes for pure states) for the same state.
 
==References==
<references/>
 
[[Category:Quantum mechanical entropy]]
[[Category:Mathematical physics]]
[[Category:Quantum mechanics]]
 
 
{{quantum-stub}}

Latest revision as of 15:51, 4 September 2014

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Term life insurance is meant to only provide money to the policy's beneficiaries in the event of the policy holder's death. To Buy Life Insurance of this type is easy: The only thing that a person needs to know to buy this term insurance is the cash amount that he can pay and the period for which the insurance he needs. Permanent Insurance) is a combination of life coverage and an investment fund. Term life insurance is typically purchased for a set amount of time and for a predetermined amount of coverage. Other qualifications are needed for anybody advising on pension transfer or income drawdown business. So a family with young children can reason that in 15 or 20 years all of the kids will have completed their education and have jobs. ve read this (hopefully wonderful) discussion about term vs whole life insurance.

Nicotine can lead to some dangerous diseases like cardiovascular disease or hypertension. Refrain from investing through life insurance policies. You simply answer a handful of quick, simple questions. It is very useful as an income replacement when the individual meets an unfortunate death. Obviously, you may need the best term life insurance policy and know your choices. The most popular term life insurance policies are the 10 year term policy, the 15 year term policy, the 20 year term policy, the 25 year term policy and the 30 year term policy. However, the rates for this policy can be higher than for term life where a medical exam is necessary.

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This can lead to benefits that are paid out to only one child instead of all of the children of an insured person, and in some documented cases it has led to an ex-spouse receiving benefits and the insured person's current spouse receiving nothing. Rates will not change based external factors such as interest rates for the life of the contract. Delays are more common than non-payment of benefits. This is very cheap insurance because when the mortgage balance goes down the face amount of the policy goes down with it. Let's consider why people buy long term care insurance. There are other options, so, is term life insurance for you. Experts say that you should be covered by term life insurance until you are 65 years old.