Concurrence (quantum computing)
Encyclopedia
In quantum computing, the concurrence is an entanglement monotone defined for a mixed state of two qubit
s as .
in which
are the eigenvalues of the Hermitian matrix
with
the spin-flipped state of
, 
a Pauli spin matrix, and the eigenvalues listed in decreasing order. Alternatively, the 
's represent the square roots of the eigenvalues of the non-Hermitian matrix 
. From the concurrence, the entanglement of formation can be calculated.
For pure states, the concurrence is a polynomial
invariant in the state's coefficients. For mixed states, the concurrence can be defined by convex roof extension.
For the concurrence, there is monogamy of entanglement, that is, the concurrence of a qubit with the rest of the system cannot ever exceed the sum of the concurrences of qubit pairs which it is part of.
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
s as .
in which
are the eigenvalues of the Hermitian matrixwith
the spin-flipped state of
, a Pauli spin matrix, and the eigenvalues listed in decreasing order. Alternatively, the 's represent the square roots of the eigenvalues of the non-Hermitian matrix . From the concurrence, the entanglement of formation can be calculated.For pure states, the concurrence is a polynomial
invariant in the state's coefficients. For mixed states, the concurrence can be defined by convex roof extension.For the concurrence, there is monogamy of entanglement, that is, the concurrence of a qubit with the rest of the system cannot ever exceed the sum of the concurrences of qubit pairs which it is part of.