We investigate the monogamy nature of entanglement in a three-qubit system. A monogamy inequality is presented to describe the exclusive relation between the $A\text{\ensuremath{-}}B$ two-qubit concurrence ${C}_{AB}$ and the $AB\text{\ensuremath{-}}C$ three-qubit concurrence ${C}_{(AB)C}$ , which represents the entanglement between qubits $\mathit{A}$ and $\mathit{B}$ as a whole and the third qubit $\mathit{C}$ . It is found that the entanglement between any two qubits in a three-qubit system is limited by the entanglement between these two qubits and another qubit. As a consequence, we present the upper bounds for the concurrence ${C}_{AB}$ , when the concurrence between qubits $\mathit{A}$ and $\mathit{C}$ $({C}_{AC})$ and the concurrence between qubits $\mathit{B}$ and $\mathit{C}$ $({C}_{BC})$ are both given or one of the two is provided.We investigate the monogamy nature of entanglement in a three-qubit system. A monogamy inequality is presented to describe the exclusive relation between the $A\text{\ensuremath{-}}B$ two-qubit concurrence ${C}_{AB}$ and the $AB\text{\ensuremath{-}}C$ three-qubit concurrence ${C}_{(AB)C}$, which represents the entanglement between qubits $\mathit{A}$ and $\mathit{B}$ as a whole and the third qubit $\mathit{C}$. It is found that the entanglement between any two qubits in a three-qubit system is limited by the entanglement between these two qubits and another qubit. As a consequence, we present the upper bounds for the concurrence ${C}_{AB}$, when the concurrence between qubits $\mathit{A}$ and $\mathit{C}$ $({C}_{AC})$ and the concurrence between qubits $\mathit{B}$ and $\mathit{C}$ $({C}_{BC})$ are both given or one of the two is provided.

Physical Review AJul 14, 200810 citations

Manipulating qubits

Michel Le Bellac

Cambridge University Press eBooksJun 15, 20061 citation

Converting qubits

Hyunseok Jeong

arXiv:2302.05581Nature PhotonicsFeb 1, 20233 citations

Entanglement increase from local interactions and not completely positive maps

Thomas F. Jordan, Anil Shaji, E. C. G. Sudarshan

Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits, and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a SWAP operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. When the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. The combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time.Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits, and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a SWAP operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. When the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. The combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time.

arXiv:0704.0461Physical Review AAug 16, 200715 citations

Computation with Qubits

WORLD SCIENTIFIC eBooksOct 28, 20130 citations

An entanglement measure for n qubits

Dafa Li, Xiangrong Li, Hongtao Huang +1 more

Coffman et al. [Phys. Rev. A 61, 052306 (2000)] introduced the residual entanglement for three qubits. In this paper, we present the entanglement measure τ(ψ) for even n qubits; for odd n qubits, we propose the residual entanglement τ(i)(ψ) with respect to qubit i and the odd n-tangle R(ψ) by averaging the residual entanglement with respect to each qubit. In this paper, we show that these measures are LU-invariant, entanglement monotones, invariant under permutations of the qubits, and multiplicative in some cases.Coffman et al. [Phys. Rev. A 61, 052306 (2000)] introduced the residual entanglement for three qubits. In this paper, we present the entanglement measure τ(ψ) for even n qubits; for odd n qubits, we propose the residual entanglement τ(i)(ψ) with respect to qubit i and the odd n-tangle R(ψ) by averaging the residual entanglement with respect to each qubit. In this paper, we show that these measures are LU-invariant, entanglement monotones, invariant under permutations of the qubits, and multiplicative in some cases.

arXiv:0710.3425Journal of Mathematical PhysicsJan 1, 200917 citations

{C}_{AB}

and the $AB\text{\ensuremath{-}}C$ three-qubit concurrence

{C}_{(AB)C}

, which represents the entanglement between qubits

\mathit{A}

and

\mathit{B}

as a whole and the third qubit

\mathit{C}

. It is found that the entanglement between any two qubits in a three-qubit system is limited by the entanglement between these two qubits and another qubit. As a consequence, we present the upper bounds for the concurrence

{C}_{AB}

, when the concurrence between qubits

\mathit{A}

and

\mathit{C}

({C}_{AC})

and the concurrence between qubits

\mathit{B}

and

\mathit{C}

({C}_{BC})

are both given or one of the two is provided.