Entanglement.DynamicEntTheory¶

Entanglement.DynamicEntTheory.MaxLogNeg(JN, dim)¶

\[LN_{\max}(\mathcal{N}) = \log \inf\{\max\{\|P_{AB}\|_{\infty}, \|P^{T_B}_{AB}\|_{\infty}\}: -P^{T_{BB'}}_{ABA'B'} \leq (J^{\mathcal{N}}_{ABA'B'})^{T_{BB'}} \leq P^{T_{BB'}}_{ABA'B'}\},\]

Parameters:¶

• JN (numeric) – The Choi matrix of the bipartite channel.

• dim (numeric) – The array storing input and output dimensions.

Returns:¶

The generalized \(\kappa\)-entanglement (or max-logarithmic negativity) of bipartite channel.

Return type:¶

numeric

Raises:¶

error – If either input/output dimension does not match, an error is raised.

Note

Wang, X., & Wilde, M. M. (2023). Exact entanglement cost of quantum states and channels under positive-partial-transpose-preserving operations. Physical Review A, 107(1), 012429.

Entanglement.DynamicEntTheory.MaxRainsInfo(JN, dim)¶

\[R^{2\rightarrow 2}_{\max}(\mathcal{N}) = \log \inf\{\|V_{AB} + Y_{AB}\|_{\infty}: (V_{ABA'B'} - Y_{ABA'B'})^{T_{BB'}} \geq J^{\mathcal{N}}_{ABA'B'}\},\]

Parameters:¶

• JN (numeric) – The Choi matrix of the bipartite channel.

• dim (numeric) – The array storing input and output dimensions.

Returns:¶

The bidirectional max-Rains information of bipartite channel.

Return type:¶

numeric

Raises:¶

error – If either input/output dimension does not match, an error is raised.

Note

Wang, X., Fang, K., & Duan, R. (2018). Semidefinite programming converse bounds for quantum communication. IEEE Transactions on Information Theory, 65(4), 2583-2592.