Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

L. M. Procopio, F. Delgado, M. Enríquez, N. Belabas, and J. A. Levenson, Communication enhancement through quantum coherent control of N channels in an indefinite causal-order scenario, Entropy 21

Original

1902

Earlier work this paper cites.

D. Trillo, B. Dive, and M. Navascués, Translating uncontrolled systems in time, Quantum 4

Original

1903

Earlier work this paper cites.

N. Paunković and M. Vojinović, Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders, Quantum 4

Original

1905

Earlier work this paper cites.

N. Loizeau and A. Grinbaum, Channel capacity enhancement with indefinite causal order, Phys. Rev. A 101

Original

1906

Earlier work this paper cites.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Probabilistic exact universal quantum circuits for transforming unitary operations, Phys. Rev. A 100

Original

1909

Earlier work this paper cites.

L. M. Procopio, F. Delgado, M. Enríquez, N. Belabas, and J. A. Levenson, Sending classical information via three noisy channels in superposition of causal orders, Phys. Rev. A 101

Original

1910

Earlier work this paper cites.

X. Zhao, Y. Yang, and G. Chiribella, Quantum Metrology with Indefinite Causal Order, Phys. Rev. Lett. 124

Original

1912

Earlier work this paper cites.

A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. 3

1972

Earlier work this paper cites.

M.-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra Its Appl. 10

1975

Earlier work this paper cites.

M. M. Taddei, J. Cariñe, D. Martínez, T. García, N. Guerrero, A. A. Abbott, M. Araújo, C. Branciard, E. S. Gómez, S. P. Walborn, et al. , Computational advantage from the quantum superposition of multiple temporal orders of photonic gates, PRX Quantum 2

Original

2002

Earlier work this paper cites.

D. Felce and V. Vedral, Quantum Refrigeration with Indefinite Causal Order, Phys. Rev. Lett. 125

Original

2003

Earlier work this paper cites.

W. Yokojima, M. T. Quintino, A. Soeda, and M. Murao, Consequences of preserving reversibility in quantum superchannels, Quantum 5

Original

2003

Earlier work this paper cites.

S. Sazim, M. Sedlak, K. Singh, and A. K. Pati, Classical communication with indefinite causal order for N completely depolarizing channels, Phys. Rev. A 103

Original

2004

Earlier work this paper cites.

H. Kristjánsson, W. Mao, and G. Chiribella, Witnessing latent time correlations with a single quantum particle, Phys. Rev. Res. 3

Original

2004

Earlier work this paper cites.

L. Hardy, Probability theories with dynamic causal structure: a new framework for quantum gravity, arXiv:gr-qc/0509120 (2005)

2005

Earlier work this paper cites.

G. Chiribella, M. Wilson, and H. F. Chau, Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders, Phys. Rev. Lett. 127

Original

2005

Earlier work this paper cites.

G. Rubino, L. A. Rozema, D. Ebler, H. Kristjánsson, S. Salek, P. A. Guérin, A. A. Abbott, C. Branciard, Č. Brukner, G. Chiribella, et al. , Experimental quantum communication enhancement by superposing trajectories, Phys. Rev. Res. 3

Original

2007

Earlier work this paper cites.

L. Hardy, Quantum gravity computers: On the theory of computation with indefinite causal structure, in Quantum reality, relativistic causality, and closing the epistemic circle (Springer, 2009) pp. 379–401, arXiv:quant-ph/0701019

2009

Earlier work this paper cites.

J. Bavaresco, M. Murao, and M. T. Quintino, Strict Hierarchy between Parallel, Sequential, and Indefinite-Causal-Order Strategies for Channel Discrimination, Phys. Rev. Lett. 127

Original

2011

Earlier work this paper cites.

X. Nie, X. Zhu, K. Huang, K. Tang, X. Long, Z. Lin, Y. Tian, C. Qiu, C. Xi, X. Yang, et al. , Experimental Realization of a Quantum Refrigerator Driven by Indefinite Causal Orders, Phys. Rev. Lett. 129

Original

2011

Earlier work this paper cites.

Z. Gavorová, M. Seidel, and Y. Touati, Topological obstructions to quantum computation with unitary oracles, Phys. Rev. A 109

Original

2011

Earlier work this paper cites.

O. Oreshkov, F. Costa, and Č. Brukner, Quantum correlations with no causal order, Nat. Commun. 3

Original

2012

Earlier work this paper cites.

T. Colnaghi, G. M. D’Ariano, S. Facchini, and P. Perinotti, Quantum computation with programmable connections between gates, Phys. Lett. A 376

Original

2012

Earlier work this paper cites.

G. Chiribella, Perfect discrimination of no-signalling channels via quantum superposition of causal structures, Phys. Rev. A 86

Original

2012

Earlier work this paper cites.

G. Chiribella, G. M. D’Ariano, P. Perinotti, and B. Valiron, Quantum computations without definite causal structure, Phys. Rev. A 88

Original

2013

Earlier work this paper cites.

Ä. Baumeler, A. Feix, and S. Wolf, Maximal incompatibility of locally classical behavior and global causal order in multiparty scenarios, Phys. Rev. A 90

Original

2014

Earlier work this paper cites.

M. Araújo, F. Costa, and Č. Brukner, Computational Advantage from Quantum-Controlled Ordering of Gates, Phys. Rev. Lett. 113

Original

2014

Cited alongside, same era.

M. Araújo, A. Feix, F. Costa, and Č. Brukner, Quantum circuits cannot control unknown operations, New J. Phys. 16

Original

2014

Cited alongside, same era.

L. M. Procopio, A. Moqanaki, M. Araújo, F. Costa, I. A. Calafell, E. G. Dowd, D. R. Hamel, L. A. Rozema, Č. Brukner, and P. Walther, Experimental superposition of orders of quantum gates, Nat. Commun. 6

Original

2015

Cited alongside, same era.

M. Araújo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and Č. Brukner, Witnessing causal nonseparability, New J. Phys. 17

Original

2015

Cited alongside, same era.

Ä. Baumeler and S. Wolf, The space of logically consistent classical processes without causal order, New J. Phys. 18

K. Goswami, Y. Cao, G. A. Paz-Silva, J. Romero, and A. G. White, Increasing communication capacity via superposition of order, Phys. Rev. Res. 2

Original

2020

Later among the works it cites.

Y. Guo, X.-M. Hu, Z.-B. Hou, H. Cao, J.-M. Cui, B.-H. Liu, Y.-F. Huang, C.-F. Li, G.-C. Guo, and G. Chiribella, Experimental Transmission of Quantum Information Using a Superposition of Causal Orders, Phys. Rev. Lett. 124

Original

2020

Later among the works it cites.

J. Wechs, H. Dourdent, A. A. Abbott, and C. Branciard, Quantum Circuits with Classical Versus Quantum Control of Causal Order, PRX Quantum 2

Original

2021

Later among the works it cites.

M. J. Renner and Č. Brukner, Reassessing the computational advantage of quantum-controlled ordering of gates, Phys. Rev. Res. 3

Original

2021

Later among the works it cites.