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Results tagged with tensor-products
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user 11236
7
votes
Accepted
Tensor product of positive linear maps is positive
No. A standard example is given by $A_1 = A_2 = B_1 = B_2 = M_2(\mathbb{C})$, where we choose $\pi_1$ to be the identity map and $\pi_2$ to be the transpose map. These maps are positive, but $\pi_1 \o …
- 6,351
4
votes
Accepted
Operation including tensor product or Kronecker product transforming matrix $A$ into matrix $B$
The linear transformation converting $A$ into $B$ is sometimes called the "realignment map" (see https://arxiv.org/abs/quant-ph/0205017, for example): it is the linear transformation $R$ with the prop …
- 6,351
11
votes
Linear algebra underlying quantum entanglement?
Many introductory books on quantum information theory go over the linear algebraic tools necessary to study the topic, including the tensor product (since it indeed models quantum entanglement). Takin …
- 6,351