# Holographic mutual information is monogamous

@article{Hayden2013HolographicMI, title={Holographic mutual information is monogamous}, author={Patrick M. Hayden and Matthew Headrick and Alexander Maloney}, journal={Physical Review D}, year={2013}, volume={87}, pages={046003} }

We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from…

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## References

SHOWING 1-10 OF 42 REFERENCES

### Holographic proof of the strong subadditivity of entanglement entropy

- Mathematics
- 2007

When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as strong subadditivity. For a field theory this inequality can be stated as follows:…

### Entanglement Renyi entropies in holographic theories

- Computer Science
- 2010

The RT formula predicts a phase transition in the entanglement entropy as a function of their separation, and that the mutual information between the intervals vanishes for separations larger than the phase transition point.

### “Squashed entanglement”: An additive entanglement measure

- Computer Science, Mathematics
- 2004

A new entanglement monotone for bipartite quantum states is presented, inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions: it is convex, additive on tensor products, and superadditive in general.

### Area laws in quantum systems: mutual information and correlations.

- PhysicsPhysical review letters
- 2008

This Letter shows that the holographic principle not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law.

### Monogamy of quantum entanglement and other correlations

- Physics
- 2004

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the ``monogamous nature of…

### Quantum, classical, and total amount of correlations in a quantum state (11 pages)

- Physics
- 2005

We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work…

### Faithful Squashed Entanglement

- Computer Science
- 2011

This paper presents a lower bound for squashed entanglement in terms of a distance to the set of separable states, and shows that multiple provers are not more powerful than a single prover when the verifier is restricted to LOCC operations thereby providing a new characterisation of the complexity class QMA.

### Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality

- Mathematics
- 2004

We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality…

### Topological entanglement entropy and holography

- Physics
- 2008

We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi. The entanglement entropy between a region and its complement is…