Area laws in quantum systems: mutual information and correlations.

By Michael M. Wolf, Frank Verstraete, M. B. Hastings, J. I. Cirac. Physical Review Letters, 2007

635 citations recorded by the source corpus.

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon 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. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c1f6aeffe3949378e6779a55b028180752e01b8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. R. Myers
2. T. Nishioka
3. Pasquale Calabrese
4. T. Takayanagi
5. J. Cardy
6. M. Headrick
7. H. Casini
8. M. Huerta

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. Pasquale Calabrese
3. T. Takayanagi
4. T. Nishioka
5. J. Cardy
6. M. Headrick
7. H. Casini
8. M. Huerta

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. D. Harlow
4. T. Nishioka
5. H. Casini
6. M. Huerta
7. S. Raju
8. Mark Van Raamsdonk

Citations in the corpus

• Bulk locality and quantum error correction in AdS/CFT (2014, background): “22) it is not difficult to show that [22]”
• Neural Network Renormalization Group (2018, background): “Note that different from the tensor network modeling of quantum states [49], the MERA-like architecture is sufficient to model classical systems with short-range interactions even at criticality since they exhibit the mutual information area law [50].”
• Holographic mutual information is monogamous (2011, neutral): “12) saturates the quantum Pinsker bound as specialized to connected correlators of normalized operators [18, 19]: ( 〈OAOB〉 − 〈OA〉〈OB〉 ‖OA‖‖OB‖ )2 ≤ 2I(A : B) .”
• Measuring entanglement entropy in a quantum many-body system (2015, background): “It is instructive to investigate the scaling of Rényi entropy and mutual information with subsystem size [13, 51] since in larger systems they can characterize quantum phases, for example by measuring the central charge of the underlying quantum field theory [11].”
• Building up spacetime with quantum entanglement (2010, neutral): “It is straightforward to prove [11] that for any operators O C and O D , acting only on the subsystems C and D , we have Thus, if we continuously vary a state such that the mutual information between C and D go to zero, then all correlations must decrease to zero also.”
• Entanglement entropy: Holography and renormalization group (2018, background): “(52) with the Schwarz inequality, one obtains the lower bound for the mutual information (Wolf et al., 2008), I(A,B) ≥ 1 2 (〈OAOB〉 − 〈OA〉〈OB〉)2 ||OA||2||OB ||2 , (53) where OA and OB are any bounded operators in the regions A and B, respectively.”