Quantum entanglement is a fundamental resource in quantum information processing, yet its quantitative characterization remains challenging, especially for mixed states. In this work, we introduce a two-parameter family of entanglement measures, referred to as the unified (q, s)-concurrence, which generalizes both the standard concurrence and the recently proposed q-concurrence. This measure is inspired by the unified entropy and provides a flexible framework for quantifying bipartite entanglement. By combining the positive partial transposition and realignment criteria, we derive an analytical lower bound for this measure for arbitrary bipartite mixed states, revealing a connection to strong separability criteria. Explicit expressions are obtained for the unified (q, s)-concurrence in the cases of isotropic and Werner states under the constraint <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$q>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$qs\ge 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mi>s</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, we explore the monogamy properties of the unified (q, s)-concurrence for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$q\ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$0\le s\le 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>s</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$1\le qs\le 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>q</mi> <mi>s</mi> <mo>≤</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, and establish an entanglement polygon inequality for any multipartite qudit system when <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$q\ge 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$qs\ge 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mi>s</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Our results provide a unified and versatile tool for entanglement quantification, with potential applications in quantum communication and multipartite entanglement theory.

Unified (q, s)-concurrence: a two-parameter family of bipartite entanglement measures

期刊论文
发表日期：

2026年6月16日

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Chen-Ming Bai,
Yu Luo

摘要

Quantum entanglement is a fundamental resource in quantum information processing, yet its quantitative characterization remains challenging, especially for mixed states. In this work, we introduce a two-parameter family of entanglement measures, referred to as the unified (q, s)-concurrence, which generalizes both the standard concurrence and the recently proposed q-concurrence. This measure is inspired by the unified entropy and provides a flexible framework for quantifying bipartite entanglement. By combining the positive partial transposition and realignment criteria, we derive an analytical lower bound for this measure for arbitrary bipartite mixed states, revealing a connection to strong separability criteria. Explicit expressions are obtained for the unified (q, s)-concurrence in the cases of isotropic and Werner states under the constraint $q>1$ $q > 1$ and $qs\ge 1$ $q s \geq 1$ . Furthermore, we explore the monogamy properties of the unified (q, s)-concurrence for $q\ge 2$ $q \geq 2$ , $0\le s\le 1$ $0 \leq s \leq 1$ and $1\le qs\le 3$ $1 \leq q s \leq 3$ , and establish an entanglement polygon inequality for any multipartite qudit system when $q\ge 1$ $q \geq 1$ and $qs\ge 1$ $q s \geq 1$ . Our results provide a unified and versatile tool for entanglement quantification, with potential applications in quantum communication and multipartite entanglement theory.