# Squashed Entanglement, $$\mathbf {k}$$k-Extendibility, Quantum Markov Chains, and Recovery Maps

@article{Li2014SquashedE, title={Squashed Entanglement, \$\$\mathbf \{k\}\$\$k-Extendibility, Quantum Markov Chains, and Recovery Maps}, author={Ke Li and Andreas J. Winter}, journal={Foundations of Physics}, year={2014}, volume={48}, pages={910-924} }

Squashed entanglement (Christandl and Winter in J. Math. Phys. 45(3):829–840, 2004) is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information (Fawzi and Renner in Commun. Math. Phys. 340(2):575–611, 2015) greatly extended and simplified in various work since, we show the converse, that a small value of squashed entanglement implies that the…

## 38 Citations

### Multipartite quantum correlations and local recoverability

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

It is proved that the MSQ discord is nearly equal to zero and the CEMI is a faithful entanglement measure, i.e. it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state.

### Amortized entanglement of a quantum channel and approximately teleportation-simulable channels

- Computer ScienceArXiv
- 2017

Many of the concepts in the paper are generalized to the setting of general resource theories, defining the amortized resourcefulness of a channel and the notion of ν-freely-simulable channels, connecting these concepts in an operational way as well.

### Squashed entanglement in infinite dimensions

- Physics, Computer Science
- 2015

It is shown that the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved and the same continuity bound is valid for theEntanglement of formation.

### Bounds on Entanglement Distillation and Secret Key Agreement for Quantum Broadcast Channels

- Computer Science, PhysicsIEEE Transactions on Information Theory
- 2016

This paper employs multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglements can be generated between any subset of the users of such a channel, along the way developing several new properties of these measures.

### On variational expressions for quantum relative entropies

- Computer ScienceArXiv
- 2015

A new variational expression is created for the measured Rényi relative entropy, which is exploited to show that certain lower bounds on quantum conditional mutual information are superadditive.

### Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures

- Mathematics, Computer ScienceArXiv
- 2015

This paper provides an alternate characterization of short quantum Markov chains and sufficient quantum channels, thus providing further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference.

### The symmetric extendibility of quantum states

- Computer Science
- 2016

This paper analyzes composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems, and introduces a new one- way entanglement monotone based on the best symmetric approximation of a quantum state and the extendible number of a Quantum state.

### Sample optimal tomography of quantum Markov chains

- Mathematics
- 2022

A state on a tripartite quantum system HA ⊗HB ⊗HC forms a Markov chain, i.e., quantum conditional independence, if it can be reconstructed from its marginal on HA ⊗HB by a quantum operation from HB…

### Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

- PhysicsSciPost Physics
- 2022

We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic…

### Monotonicity of quantum relative entropy and recoverability

- MathematicsQuantum Inf. Comput.
- 2015

A remainder term is established that quantifies how well one can recover from a loss of information by employing a rotated Petz recovery map, and it is shown that the monotonicity of relative entropy with respect to quantum operations is equivalent to each of the following inequalities.

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