# Private quantum codes: introduction and connection with higher rank numerical ranges

@article{Kribs2014PrivateQC, title={Private quantum codes: introduction and connection with higher rank numerical ranges}, author={David W. Kribs and Sarah Plosker}, journal={Linear and Multilinear Algebra}, year={2014}, volume={62}, pages={639 - 647} }

We give a brief introduction to private quantum codes, a basic notion in quantum cryptography and key distribution. Private code states are characterized by indistinguishability of their output states under the action of a quantum channel, and we show that higher rank numerical ranges can be used to describe them. We also show how this description arises naturally via conjugate channels and the bridge between quantum error correction and cryptography.

## 3 Citations

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The connection between quantum error correction and quantum cryptography through the notion of conjugate (or complementary) channels is explored and trumping is characterized through the complete monotonicity of certain Dirichlet polynomials corresponding to quantum states.

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This paper proves that for every positive integer n, there exists an n-qubit Pauli channel for which any non-trivial quantum clique or quantum anti-clique fails to be a stabilizer code.

### Higher Rank Numerical Ranges For Certain Non-Normal Matrices

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This thesis undertakes the study of higher rank numerical ranges for certain nonnormal matrices, namely direct sums of Jordan blocks T = ⊕m j=1 Jnj(α), and direct sums of the form T = Jn(α) ⊕ βIm.…

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