Wootters [Phys. Rev. Lett. $80,$ 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with $d>~3).$ The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit $(d=3);$ the generalization to $d>3$ then follows readily.Wootters [Phys. Rev. Lett. $80,$ 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with $d>~3).$ The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit $(d=3);$ the generalization to $d>3$ then follows readily.

arXiv:quant-ph/0301015Physical Review AMay 23, 200357 citations

Entanglement of formation and monogamy of multi-party quantum entanglement

Jeong San Kim

We provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical-classical-quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems of arbitrary dimensions.We provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical-classical-quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems of arbitrary dimensions.

arXiv:2101.05590Scientific ReportsJan 27, 20219 citations

Entanglement of formation for a class of quantum states

Shao-Ming Fei, Jürgen Jost, Xianqing Li‐Jost +1 more

arXiv:quant-ph/0304095Physics Letters AApr 1, 200343 citations

Entanglement of Pure States

Stig Stenholm

Foundations of PhysicsJan 26, 20090 citations

Entanglement of Formation for Gaussian States

J. Solomon Ivan, R. Simon

The entanglement of formation (EOF) is computed for arbitrary two-mode Gaussian states. Apart from a conjecture, our analysis rests on two main ingredients. The first is a four-parameter canonical form we develop for the covariance matrix, one of these parameters acting as a measure of EOF, and the second is a generalisation of the EPR correlation, used in the work of Giedke {\em et al} [Phys. Rev. Lett. {\bf 91}, 107901 (2003)], to noncommuting variables. The conjecture itself is in respect of an extremal property of this generalized EPR correlation.The entanglement of formation (EOF) is computed for arbitrary two-mode Gaussian states. Apart from a conjecture, our analysis rests on two main ingredients. The first is a four-parameter canonical form we develop for the covariance matrix, one of these parameters acting as a measure of EOF, and the second is a generalisation of the EPR correlation, used in the work of Giedke {\em et al} [Phys. Rev. Lett. {\bf 91}, 107901 (2003)], to noncommuting variables. The conjecture itself is in respect of an extremal property of this generalized EPR correlation.

arXiv:0808.1658Aug 12, 20083 citations

Wootters [Phys. Rev. Lett.

80,

2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with

d>~3).

The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit

(d=3);

the generalization to

d>3

then follows readily.