Approximating the Distribution of Schmidt Vector Norms
Recently, a family of vector norms [1,2] have been introduced in quantum information theory that are useful for helping classify entanglement of quantum states. In particular, the Schmidt vector k-norm...
View ArticleThe Other Superoperator Isomorphism
A few months ago, I spent two posts describing the Choi-Jamiolkowski isomorphism between linear operators from Mn to Mm (often referred to as “superoperators“) and linear operators living in the space...
View ArticleSeparability-Preserving Operators in Entanglement Theory
One of the key concepts in quantum information theory is the difference between separable states and entangled states. A pure quantum state (that is, a unit vector) v ∈ Cn ⊗ Cn is said to be separable...
View ArticleMATLAB Scripts for Computing Completely Bounded Norms via Semidefinite...
In operator theory, the completely bounded norm of a linear map on complex matrices is defined by , where is the usual norm on linear maps defined by and is the operator norm of [1]. The completely...
View ArticleNorms and Dual Norms as Supremums and Infimums
Let be a finite-dimensional Hilbert space over or (the fields of real and complex numbers, respectively). If we let be a norm on (not necessarily the norm induced by the inner product), then the dual...
View ArticleHow to Construct Minimal Unextendible Product Bases
In quantum information theory, a product state is a quantum state that can be written as an elementary tensor: while states that can not be written in this form are called entangled. In this post, we...
View ArticleThe Spectrum of the Partial Transpose of a Density Matrix
It is a simple fact that, given any density matrix (i.e., quantum state) , the eigenvalues of are the same as the eigenvalues of (the transpose of ). However, strange things can happen if we instead...
View ArticleIn Search of a 4-by-11 Matrix
After spinning my wheels on a problem for far too long, I’ve decided that it’s time to enlist the help of the mathematical and programming geniuses of the world wide web. The problem I’m interested in...
View ArticleIntroducing QETLAB: A MATLAB toolbox for quantum entanglement
After over two and a half years in various stages of development, I am happy to somewhat “officially” announce a MATLAB package that I have been developing: QETLAB (Quantum Entanglement Theory...
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