Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits

S. Gopalakrishnan and A. Lamacraft, Unitary circuits of finite depth and infinite width from quantum channels , Phys. Rev. B 100

Original

1903

Earlier work this paper cites.

B. Bertini, P. Kos and T. Prosen, Exact Correlation Functions for Dual-Unitary Lattice Models in 1 +1 Dimensions , Phys. Rev. Lett. 123

Original

1904

Earlier work this paper cites.

N. Hunter-Jones, Unitary designs from statistical mechanics in random quantum circuits , arXiv e-prints (2019) arXiv:1905.12053 [ 1905.12053 ]

Original

1905

Earlier work this paper cites.

S. Pilatowsky-Cameo, J. Chávez-Carlos, M.A. Bastarrachea-Magnani, P. Stránský, S. Lerma-Hernández, L.F. Santos et al., Positive quantum Lyapunov exponents in experimental systems with a regular classical limit , Phys. Rev. E 101

Original

1909

Earlier work this paper cites.

B. Bertini, P. Kos and T. Prosen, Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits , SciPost Physics 8

Original

1909

Earlier work this paper cites.

G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior , arXiv e-prints (2019) arXiv:1911.11977 [ 1911.11977 ]

Original

1911

Earlier work this paper cites.

T. Xu, T. Scaffidi and X. Cao, Does Scrambling Equal Chaos? , Phys. Rev. Lett. 124

Original

1912

Earlier work this paper cites.

A.W. Harrow and R.A. Low, Random Quantum Circuits are Approximate 2-designs , Communications in Mathematical Physics 291

Original

1919

Earlier work this paper cites.

A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators , Reports on mathematical physics 3

1972

Earlier work this paper cites.

M.-D. Choi, Completely positive linear maps on complex matrices , Linear algebra and its applications 10

1975

Earlier work this paper cites.

R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution , Mathematische Annalen 298

1994

Earlier work this paper cites.

D. Voiculescu, The analogues of entropy and of fisher’s information measure in free probability theory iii: The absence of cartan subalgebras , Geometric & Functional Analysis GAFA 6

1996

Earlier work this paper cites.

D.V. Voiculescu, Free probability theory , vol. 12, American Mathematical Soc. (1997)

1997

Earlier work this paper cites.

L. Ge, Applications of free entropy to finite von neumann algebras, ii , Annals of Mathematics 147

1998

Earlier work this paper cites.

D. Voiculescu, Free Entropy , arXiv Mathematics e-prints (2001) math/0103168 [ math/0103168 ]

2001

Earlier work this paper cites.

L. Ge and J. Shen, On free entropy dimension of finite von neumann algebras , Geometric & Functional Analysis GAFA 12

2002

Earlier work this paper cites.

P.W. Claeys and A. Lamacraft, Maximum velocity quantum circuits , Physical Review Research 2

Original

2003

Earlier work this paper cites.

K. Zyczkowski and I. Bengtsson, On duality between quantum maps and quantum states , arXiv e-prints (2004) quant [ quant-ph/0401119 ]

2004

Earlier work this paper cites.

M. Stefan, Indecomposability of free group factors over nonprime subfactors and abelian subalgebras , arXiv Mathematics e-prints (2004) math/0402108 [ math/0402108 ]

2004

Earlier work this paper cites.

J.A. Mingo and R. Speicher, Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces , arXiv Mathematics e-prints (2004) math/0405191 [ math/0405191 ]

2004

Earlier work this paper cites.

J.A. Mingo, P. Sniady and R. Speicher, Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices , arXiv Mathematics e-prints (2004) math/0405258 [ math/0405258 ]

2004

Earlier work this paper cites.

F. Hiai and D. Petz, Large deviations for functions of two random projection matrices , arXiv Mathematics e-prints (2005) math/0504435 [ math/0504435 ]

2005

Earlier work this paper cites.

A. Nica and R. Speicher, Lectures on the combinatorics of free probability , vol. 13, Cambridge University Press (2006)

2006

Earlier work this paper cites.

D. Armstrong, Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups , arXiv Mathematics e-prints (2006) math/0611106 [ math/0611106 ]

2006

Earlier work this paper cites.

F. Hiai and Y. Ueda, Notes on microstate free entropy of projections , arXiv Mathematics e-prints (2006) math/0605633 [ math/0605633 ]

2006

Earlier work this paper cites.

B. Collins, J.A. Mingo, P. Sniady and R. Speicher, Second Order Freeness and Fluctuations of Random Matrices, III. Higher order freeness and free cumulants , arXiv Mathematics e-prints (2006) math/0606431 [ math/0606431 ]

2006

Earlier work this paper cites.

A. Bhattacharyya, W. Chemissany, S.S. Haque, J. Murugan and B. Yan, The multi-faceted inverted harmonic oscillator: Chaos and complexity , SciPost Physics Core 4

Original

2007

Earlier work this paper cites.

K. Hashimoto, K.-B. Huh, K.-Y. Kim and R. Watanabe, Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator , Journal of High Energy Physics 2020

Original

2007

Earlier work this paper cites.

B. Collins, I. Nechita and K. Życzkowski, Random graph states, maximal flow and Fuss-Catalan distributions , Journal of Physics A Mathematical General 43

Original

2010

Earlier work this paper cites.

R. Movassagh and A. Edelman, Isotropic Entanglement , arXiv e-prints (2010) arXiv:1012.5039 [ 1012.5039 ]

Original

2010

Earlier work this paper cites.

J. Cotler, N. Hunter-Jones and D. Ranard, Fluctuations of subsystem entropies at late times , arXiv e-prints (2020) arXiv:2010.11922 [ 2010.11922 ]

Original

2010

Cited alongside, same era.

R. Movassagh and A. Edelman, Density of States of Quantum Spin Systems from Isotropic Entanglement , Phys. Rev. Lett. 107

Original

2011

Cited alongside, same era.

J. Chen, E. Hontz, J. Moix, M. Welborn, T. Van Voorhis, A. Suárez et al., Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems , Phys. Rev. Lett. 109

Original

2012

Cited alongside, same era.

M. Musz, M. Kuś and K. Życzkowski, Unitary quantum gates, perfect entanglers, and unistochastic maps , Phys. Rev. A 87

Original

2013

Cited alongside, same era.

S.H. Shenker and D. Stanford, Black holes and the butterfly effect , Journal of High Energy Physics 2014

C.W. von Keyserlingk, T. Rakovszky, F. Pollmann and S.L. Sondhi, Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws , Physical Review X 8

Original

2018

Later among the works it cites.

A. Nahum, S. Vijay and J. Haah, Operator Spreading in Random Unitary Circuits , Physical Review X 8

Original

2018

Later among the works it cites.

S. Pappalardi, A. Russomanno, B. Žunkovič, F. Iemini, A. Silva and R. Fazio, Scrambling and entanglement spreading in long-range spin chains , Phys. Rev. B 98

Original

2018

Later among the works it cites.

Q. Hummel, B. Geiger, J.D. Urbina and K. Richter, Reversible quantum information spreading in many-body systems near criticality , arXiv e-prints (2018) arXiv:1812.09237 [ 1812.09237 ]

Original

2018

Later among the works it cites.