SkVectorNorm: Difference between revisions
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|name=SkVectorNorm | |name=SkVectorNorm | ||
|desc=Computes the [[s(k)-vector norm|s(k)-norm of a vector]] | |desc=Computes the [[s(k)-vector norm|s(k)-norm of a vector]] | ||
| | |rel=[[KyFanNorm]]<br />[[SchmidtDecomposition]]<br />[[SkOperatorNorm]] | ||
|cat=[[List of functions#Norms|Norms]] | |||
|upd=December 2, 2012 | |upd=December 2, 2012 | ||
|v= | |v=0.50}} | ||
<tt>'''SkVectorNorm'''</tt> is a [[List of functions|function]] that computes the [[s(k)-vector norm|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>). | <tt>'''SkVectorNorm'''</tt> is a [[List of functions|function]] that computes the [[s(k)-vector norm|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>). | ||
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===Sum of squares of eigenvalues of reduced density matrix=== | ===Sum of squares of eigenvalues of reduced density matrix=== | ||
The square of the s(k)-vector norm is equal to the [[Ky Fan norm|Ky Fan k-norm]] of the vector's reduced density matrix: | The square of the s(k)-vector norm is equal to the [[Ky Fan norm|Ky Fan k-norm]] of the vector's reduced density matrix: | ||
< | <syntaxhighlight> | ||
>> v = | >> v = RandomStateVector(9); | ||
>> [SkVectorNorm(v,1)^2, | >> [SkVectorNorm(v,1)^2, KyFanNorm(PartialTrace(v*v'),1)] | ||
ans = | ans = | ||
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1.0000 1.0000 | 1.0000 1.0000 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=SkVectorNorm}} | |||
==References== | ==References== | ||
<references /> | <references /> | ||
Revision as of 17:16, 22 September 2014
| SkVectorNorm | |
| Computes the s(k)-norm of a vector | |
| Other toolboxes required | none |
|---|---|
| Related functions | KyFanNorm SchmidtDecomposition SkOperatorNorm |
| Function category | Norms |
SkVectorNorm is a function that computes the s(k)-norm of a vector (i.e., the Euclidean norm of the vector of its k largest Schmidt coefficients[1]).
Syntax
- SkVectorNorm(VEC)
- SkVectorNorm(VEC,K)
- SkVectorNorm(VEC,K,DIM)
Argument descriptions
- VEC: A vector living in bipartite space.
- K (optional, default 1): A positive integer.
- DIM (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that VEC lives on.
Examples
Sum of squares of eigenvalues of reduced density matrix
The square of the s(k)-vector norm is equal to the Ky Fan k-norm of the vector's reduced density matrix:
>> v = RandomStateVector(9);
>> [SkVectorNorm(v,1)^2, KyFanNorm(PartialTrace(v*v'),1)]
ans =
0.7754 0.7754
>> [SkVectorNorm(v,2)^2, KyFanNorm(PartialTrace(v*v'),2)]
ans =
0.9333 0.9333
>> [SkVectorNorm(v,3)^2, KyFanNorm(PartialTrace(v*v'),3)]
ans =
1.0000 1.0000Source code
Click here to view this function's source code on github.
References
- ↑ N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. J. Math. Phys., 51:082202, 2010. E-print: arXiv:0909.3907 [quant-ph]