Difference between revisions of "SkVectorNorm"

	SkVectorNorm
	Computes the s(k)-norm of a vector
Other toolboxes required	opt_args; SchmidtDecomposition
Related functions	KyFanNorm; SkOperatorNorm

Revision as of 15:34, 2 December 2012

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    1.0000

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]

[1] 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]

[1]

@@ Line 4: / Line 4: @@
 |req=[[opt_args]]<br />[[SchmidtDecomposition]]
 |rel=[[KyFanNorm]]<br />[[SkOperatorNorm]]
-|upd=November 18, 2012
+|upd=December 2, 2012
-|v=1.00}}
+|v=1.01}}
-<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.</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>).
 ==Syntax==