Abstract Quantum entanglement in multipartite systems exhibits a unique restriction on its distribution among subsystems, a fundamental property known as the monogamy of entanglement. Traditionally, monogamy has been quantified for measures such as concurrence through summation-form inequalities. Recently, it has been discovered that concurrence also obeys monogamy constraints expressed via product-form inequalities. In this work, we establish enhanced monogamy inequalities for the ν th power of concurrence (with ν ⩾ 2 ). We demonstrate, through explicit examples, that these new inequalities provide tighter bounds than existing product-form results. Furthermore, we show that our findings remain applicable to monogamy relations in high-dimensional systems.Abstract Quantum entanglement in multipartite systems exhibits a unique restriction on its distribution among subsystems, a fundamental property known as the monogamy of entanglement. Traditionally, monogamy has been quantified for measures such as concurrence through summation-form inequalities. Recently, it has been discovered that concurrence also obeys monogamy constraints expressed via product-form inequalities. In this work, we establish enhanced monogamy inequalities for the ν th power of concurrence (with ν ⩾ 2 ). We demonstrate, through explicit examples, that these new inequalities provide tighter bounds than existing product-form results. Furthermore, we show that our findings remain applicable to monogamy relations in high-dimensional systems.

Laser Physics LettersMay 1, 20260 citations

Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

Jeong San Kim, Anirban Das, Barry C. Sanders

We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MOE). We show that all proven MOE relations using concurrence can be rephrased in terms of CREN. Furthermore, we show that higher-dimensional (qudit) extensions of MOE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MOE in terms of concurrence. We further test the CREN version of MOE for qudits by considering fully or partially coherent mixtures of a qudit $W$ -class state with the vacuum and show that the CREN version of MOE for qudits is satisfied in this case as well. The CREN version of MOE for qudits is thus a strong conjecture with no obvious counterexamples.We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MOE). We show that all proven MOE relations using concurrence can be rephrased in terms of CREN. Furthermore, we show that higher-dimensional (qudit) extensions of MOE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MOE in terms of concurrence. We further test the CREN version of MOE for qudits by considering fully or partially coherent mixtures of a qudit $W$-class state with the vacuum and show that the CREN version of MOE for qudits is satisfied in this case as well. The CREN version of MOE for qudits is thus a strong conjecture with no obvious counterexamples.

arXiv:0811.2047Physical Review AJan 30, 2009208 citations

Monogamy of Entanglement of Maximal Dimension

Sumit Nandi

Abstract In the present study, a trade off of sharing of entanglement between subsystems of a higher dimensional quantum state is derived. It is presented in terms of an inequality which is analogous to the Coffman–Kundu–Wootters inequality that succinctly describes monogamy of entanglement in dimensional pure state. To derive the monogamy inequality in dimension, G‐concurrence measure of entanglement is considered as a measure of entanglement of maximal dimension. The approach of the present study incidentally points toward a rigorous framework which enables to obtain an upper bound of G‐concurrence of a bipartite qudit mixed state. Obtained upper bound of G‐concurrence is then shown to satisfy a monogamy relation.Abstract In the present study, a trade off of sharing of entanglement between subsystems of a higher dimensional quantum state is derived. It is presented in terms of an inequality which is analogous to the Coffman–Kundu–Wootters inequality that succinctly describes monogamy of entanglement in dimensional pure state. To derive the monogamy inequality in dimension, G‐concurrence measure of entanglement is considered as a measure of entanglement of maximal dimension. The approach of the present study incidentally points toward a rigorous framework which enables to obtain an upper bound of G‐concurrence of a bipartite qudit mixed state. Obtained upper bound of G‐concurrence is then shown to satisfy a monogamy relation.

arXiv:2204.13649Annalen der PhysikSep 16, 20250 citations

W

-class state with the vacuum and show that the CREN version of MOE for qudits is satisfied in this case as well. The CREN version of MOE for qudits is thus a strong conjecture with no obvious counterexamples.