We prove that the entangling capacity of a two-qubit unitary operator without local ancillas, both with and without the restriction to initial product states, as quantified by the maximum attainable concurrence, is directly related to the distinguishability of a closely related pair of two-qubit unitary operators. These operators are the original operator transformed into its canonical form and the adjoint of this canonical form. The distinguishability of these operators is quantified by the minimum overlap of the output states over all possible input probe states. The entangling capacity of the original unitary operator is therefore directly related to the degree of non-Hermiticity of its canonical form, as quantified in an operationally satisfactory manner in terms of the extent to which it can be distinguished, by measurement, from its adjoint. Furthermore, the maximum entropy of entanglement, again without local ancillas, that a given two-qubit unitary operator can generate is found to be closely related to the classical capacities of certain quantum channels.We prove that the entangling capacity of a two-qubit unitary operator without local ancillas, both with and without the restriction to initial product states, as quantified by the maximum attainable concurrence, is directly related to the distinguishability of a closely related pair of two-qubit unitary operators. These operators are the original operator transformed into its canonical form and the adjoint of this canonical form. The distinguishability of these operators is quantified by the minimum overlap of the output states over all possible input probe states. The entangling capacity of the original unitary operator is therefore directly related to the degree of non-Hermiticity of its canonical form, as quantified in an operationally satisfactory manner in terms of the extent to which it can be distinguished, by measurement, from its adjoint. Furthermore, the maximum entropy of entanglement, again without local ancillas, that a given two-qubit unitary operator can generate is found to be closely related to the classical capacities of certain quantum channels.

arXiv:quant-ph/0502083Physical Review AOct 27, 200528 citations

Entanglement of mixed states in systems of n qubits

Renán Cabrera, W. E. Baylis

Bulletin of the American Physical SocietyJun 7, 20070 citations

Simulating a single-qubit channel using a mixed-state environment

Geetu Narang, Arvind

We analyze the class of single-qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that $\frac{3}{8}$ of the generalized depolarizing channels can be simulated by the one-qubit mixed-state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli channel cannot be simulated by a one-qubit mixed-state environment.We analyze the class of single-qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that $\frac{3}{8}$ of the generalized depolarizing channels can be simulated by the one-qubit mixed-state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli channel cannot be simulated by a one-qubit mixed-state environment.

arXiv:quant-ph/0611058Physical Review AMar 5, 200717 citations

Entanglement transformation between two-qubit mixed states by LOCC

Dechao Li

Physics Letters AAug 6, 20095 citations

\frac{3}{8}

of the generalized depolarizing channels can be simulated by the one-qubit mixed-state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli channel cannot be simulated by a one-qubit mixed-state environment.