Optimized generalized monogamy relations and upper bounds for N-qubit systems

Abstract We present optimized generalized monogamy relations and upper bounds derived from concurrence and concurrence of assistance. We first establish a tighter general upper bound of the α th ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mtext>⩽</mml:mtext> <mml:mi>α</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> ) power of concurrence for N -qubit states. Then for N -qubit systems <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>B</mml:mi> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>…</mml:mo> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , the optimized monogamy relations and upper bounds satisfied by the α th ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mtext>⩽</mml:mtext> <mml:mi>α</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> ) power of concurrence of N -qubit pure states under the partition AB and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>…</mml:mo> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , as well as under the partition ABC 1 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>…</mml:mo> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> are established, which give rise to restrictions on the entanglement distribution and trade offs among the subsystems. Moreover, the utilization of the W -class states demonstrates that our results are tighter compared with the existing results. Similar results are also obtained for negativity.