The unified entropy as a promotion of the von Neumann entropy exhibits distinct diversity which contains the Tsallis entropy, the Rényi entropy, the von Neumann entropy as special cases. The unified-( $r,t$ ) entropy entanglement with $0<r<1$ and $0< t\leq 1$ was shown to be an entanglement monotone in literature. In this paper, we explore unified-( $q,s$ ) entropy entanglement with $q>1$ and $qs\geq1$ and show that it is also an entanglement monotone and that both of them are monogamous. Going further, we present two kinds of global multipartite entanglement measures (GlMEMs) based on the unified entropy and each kind has two subclasses which are classified by the parameters $(q,s)$ and $(r,t)$ . Consequently, from the view of the complete multipartite entanglement measure theory, we show that one of them is a complete multipartite entanglement monotone and is not only completely monogamous but also tightly completely monogamous, but the other three are even not complete. We also explore the genuine entanglement measures induced by the unified entropy and the relations with the bipartite entanglement and the global entanglement are discussed, respectively.The unified entropy as a promotion of the von Neumann entropy exhibits distinct diversity which contains the Tsallis entropy, the Rényi entropy, the von Neumann entropy as special cases. The unified-($r,t$) entropy entanglement with $0<r<1$ and $0< t\leq 1$ was shown to be an entanglement monotone in literature. In this paper, we explore unified-($q,s$) entropy entanglement with $q>1$ and $qs\geq1$ and show that it is also an entanglement monotone and that both of them are monogamous. Going further, we present two kinds of global multipartite entanglement measures (GlMEMs) based on the unified entropy and each kind has two subclasses which are classified by the parameters $(q,s)$ and $(r,t)$. Consequently, from the view of the complete multipartite entanglement measure theory, we show that one of them is a complete multipartite entanglement monotone and is not only completely monogamous but also tightly completely monogamous, but the other three are even not complete. We also explore the genuine entanglement measures induced by the unified entropy and the relations with the bipartite entanglement and the global entanglement are discussed, respectively.

quant-pharXiv:2605.22150May 22, 20260 citations

Entropy of Entanglement

Dominik Janzing

Compendium of Quantum PhysicsJan 1, 200917 citations

Timelike entanglement entropy and TT¯ deformation

Xin Jiang, Peng Wang, Houwen Wu +1 more

In a previous work [Eur. Phys. J. C 80, 1117 (2020)] about the $T\overline{T}$ deformed ${\mathrm{CFT}}_{2}$ , from the consistency requirement of the entanglement entropy, we found that, in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Motivated by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the $T\overline{T}$ deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies.In a previous work [Eur. Phys. J. C 80, 1117 (2020)] about the $T\overline{T}$ deformed ${\mathrm{CFT}}_{2}$, from the consistency requirement of the entanglement entropy, we found that, in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Motivated by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the $T\overline{T}$ deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies.

Physical review. D/Physical review. D.Aug 10, 202315 citations

Entanglement Entropy

WORLD SCIENTIFIC eBooksMar 10, 20260 citations

Timelike entanglement entropy and $T\bar{T}$ deformationTimelike entanglement entropy and $T\bar{T}$ deformation

Xin Jiang, Peng Wang, Houwen Wu +1 more

In a previous work arXiv:1811.07758 about the $T\bar{T}$ deformed CFT $_2$ , from the consistency requirement of the entanglement entropy theory, we found that in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Inspired by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the $T\bar{T}$ deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies.In a previous work arXiv:1811.07758 about the $T\bar{T}$ deformed CFT$_2$, from the consistency requirement of the entanglement entropy theory, we found that in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Inspired by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the $T\bar{T}$ deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies.

arXiv:2302.13872Feb 27, 20231 citation

Entanglement entropy

Manuela Kulaxizi

Modave Summer School in Mathematical PhysicsApr 24, 20140 citations

r,t

) entropy entanglement with

0<r<1

and

0< t\leq 1

was shown to be an entanglement monotone in literature. In this paper, we explore unified-(

q,s

) entropy entanglement with

q>1

and

qs\geq1

and show that it is also an entanglement monotone and that both of them are monogamous. Going further, we present two kinds of global multipartite entanglement measures (GlMEMs) based on the unified entropy and each kind has two subclasses which are classified by the parameters

(q,s)

and

(r,t)

. Consequently, from the view of the complete multipartite entanglement measure theory, we show that one of them is a complete multipartite entanglement monotone and is not only completely monogamous but also tightly completely monogamous, but the other three are even not complete. We also explore the genuine entanglement measures induced by the unified entropy and the relations with the bipartite entanglement and the global entanglement are discussed, respectively.

In a previous work [Eur. Phys. J. C 80, 1117 (2020)] about the

T\overline{T}

deformed

{\mathrm{CFT}}_{2}

, from the consistency requirement of the entanglement entropy, we found that, in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Motivated by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the

T\overline{T}

deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies.

Timelike entanglement entropy and

T\bar{T}

deformation

In a previous work arXiv:1811.07758 about the

T\bar{T}

deformed CFT

_2

, from the consistency requirement of the entanglement entropy theory, we found that in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Inspired by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the

T\bar{T}