RECORD
Quantifying the unextendibility of entanglement
Quantum Physics · Submitted 18 Nov 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. | contribution 1.00 | 0.91 | 0.08 | asserted 0.96 |
| s2 | First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. | contribution 0.84 | 0.95 | 0.09 | asserted 1.00 |
| s3 | The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. | interpretation 0.94 | 0.19 | 0.06 | asserted 0.96 |
| s4 | Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. | result 0.92 | 0.96 | 0.17 | asserted 1.00 |
| s5 | Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. | result 0.69 | 0.94 | 0.07 | asserted 1.00 |
| s6 | We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation. | result 0.85 | 0.95 | 0.33 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.
Human review
How the literature uses it
13 arXiv papers cite this in 40 sentences
Papers citing it · 30 sentences without a confident label
Uses its method or tool 1 paper
-
The resource theory of unextendible entanglement developed in [ref] serves as the primary mathematical framework in our investigation.
Extendibility limits quantum-secured communication and key distillation · Methods used in this work · 0.99
Cites it as background 6 papers
-
The unextendible entanglement of states was studied in detail in [ref] for several different underlying divergences, with applications in finding efficiently computable upper bounds on the probabilistic and exact one-way distillable entanglement and key of a state.
Extendibility limits quantum-secured communication and key distillation · Smooth-min unextendible entanglement · 0.93
-
The generalized unextendible entanglement of a bipartite state has been defined in [ref] .
Unextendible entanglement of quantum channels · Generalized unextendible entanglement of quantum states · 0.90
-
Another well known approach considers $k$-extendibility of a state [ref] , with related quantifiers proposed in [ref] .
Cycle Index Polynomials and Generalized Quantum Separability Tests · Introduction · 1.00
What it cites · 3 sentences without a confident label
Uses data or values from 1 paper
-
Note that the relative entropy of entanglement for qubit-qubit isotropic states ($d=2$) was calculated in [ref] .
Quantifying Entanglement · Examples · 0.84
Cites as background 4 papers
-
Recall that the generalized mutual information of a state $ρ_AB$ is defined as follows [ref] : [equation] where $𝐃$ is the generalized divergence discussed in Section [ref] and the infimum is with respect to every density operator $σ_B$.
On the strong converses for the quantum channel capacity theorems · Private states and unextendible entanglement · 0.82
-
Examples of interest are the quantum relative entropy [ref] , the Petz-Rényi relative entropies [ref] , the sandwiched Rényi relative entropies [ref] , and the geometric Rényi relative entropies [ref] .
Geometric R\'{e}nyi Divergence and its Applications in Quantum Channel Capacities · Quantum divergences · 0.92
-
Unextendibility arises in the contexts of Bell inequalities [ref] , quantum key distribution [ref] , and quantum communication [ref] .
Semidefinite programming hierarchies for constrained bilinear optimization · Introduction · 0.80
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.