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The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem.
Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiołkowski · 1972
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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Quantum bayesian nets
Robert R Tucci · 1995
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Causal and localizable quantum operations
David Beckman, Daniel Gottesman, M. A. Nielsen, and John Preskill · 2001
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Semicausal operations are semilocalizable
T Eggeling, D Schlingemann, and R. F Werner · 2002
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Reversible quantum cellular automata
B. Schumacher and R. F. Werner · 2004
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A categorical semantics of quantum protocols
Samson Abramsky and Bob Coecke · 2004
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Probability theories with dynamic causal structure: a new framework for quantum gravity
Lucien Hardy · 2005
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Locality and information transfer in quantum operations
Benjamin Schumacher and Michael D. Westmoreland · 2005
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Causality and tsirelson’s bounds
H. Buhrman and S. Massar · 2005
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Properties of quantum nonsignaling boxes
M. Piani, M. Horodecki, P. Horodecki, and R. Horodecki · 2006
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A categorical quantum logic
Samson Abramsky and Ross Duncan · 2006
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Factorization of quantum density matrices according to bayesian and markov networks
Robert R. Tucci · 2007
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Transforming quantum operations: Quantum supermaps
G. Chiribella, G. M. D’Ariano, and P. Perinotti · 2008
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One-dimensional quantum cellular automata over finite, unbounded configurations
Pablo Arrighi, Vincent Nesme, and Reinhard Werner · 2008
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The Two-State Vector Formalism: An Updated Review , pages 399–447
Yakir Aharonov and Lev Vaidman · 2008
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Theoretical framework for quantum networks
Giulio Chiribella, Giacomo Mauro D’Ariano, and Paolo Perinotti · 2009
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Multiple-time states and multiple-time measurements in quantum mechanics
Yakir Aharonov, Sandu Popescu, Jeff Tollaksen, and Lev Vaidman · 2009
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Generalised Proof-Nets for Compact Categories with Biproducts , pages 70–134
Ross Duncan · 2009
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Unitarity plus causality implies localizability
Pablo Arrighi, Vincent Nesme, and Reinhard Werner · 2010
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Perfect discrimination of no-signalling channels via quantum superposition of causal structures
Giulio Chiribella · 2012
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Quantum correlations with no causal order
Ognyan Oreshkov, Fabio Costa, and Caslav Brukner · 2012
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Isolation and information flow in quantum dynamics
Benjamin Schumacher and Michael D Westmoreland · 2012
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Jamie Vicary · 2012
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Quantum computations without definite causal structure
Giulio Chiribella, Giacomo Mauro D’Ariano, Paolo Perinotti, and Benoit Valiron · 2013
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Towards a formulation of quantum theory as a causally neutral theory of bayesian inference
M. S. Leifer and Robert W. Spekkens · 2013
Quantum causal modelling
Fabio Costa and Sally Shrapnel · 2016
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Exponential communication complexity advantage from quantum superposition of the direction of communication
Philippe Allard Guérin, Adrien Feix, Mateus Araújo, and Časlav Brukner · 2016
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Special relativity in a discrete quantum universe
Alessandro Bisio, Giacomo Mauro D’Ariano, and Paolo Perinotti · 2016
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Operational quantum theory without predefined time
Ognyan Oreshkov and Nicolas J Cerf · 2016
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Causal and causally separable processes
Ognyan Oreshkov and Christina Giarmatzi · 2016
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Quantum common causes and quantum causal models
John-Mark A. Allen, Jonathan Barrett, Dominic C. Horsman, Ciarán M. Lee, and Robert W. Spekkens · 2017
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Causal structure of the entanglement renormalization ansatz
Cédric Bény · 2013
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When is a quantum cellular automaton (qca) a quantum lattice gas automaton (qlga)?
Asif Shakeel and Peter J Love · 2013
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Causal categories: relativistically interacting processes
Bob Coecke and Raymond Lal · 2013
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Causal structures from entropic information: geometry and novel scenarios
Rafael Chaves, Lukas Luft, and David Gross · 2014
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Quantum causality
Caslav Brukner · 2014
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Causal fermions in discrete space-time
Terence C. Farrelly and Anthony J. Short · 2014
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Causal boxes: Quantum information-processing systems closed under composition
Christopher Portmann, Christian Matt, Ueli Maurer, Renato Renner, and Björn Tackmann · 2017
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Quantum causal graph dynamics
Pablo Arrighi and Simon Martiel · 2017
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Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning
Bob Coecke and Aleks Kissinger · 2017
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Equivalence of relativistic causal structure and process terminality
Aleks Kissinger, Matty Hoban, and Bob Coecke · 2017
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Connecting processes with indefinite causal order and multi-time quantum states
Ralph Silva, Yelena Guryanova, Anthony J Short, Paul Skrzypczyk, Nicolas Brunner, and Sandu Popescu · 2017
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Towards device-independent information processing on general quantum networks
Ciarán M. Lee and Matty J. Hoban · 2018
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Shaded tangles for the design and verification of quantum circuits
David J Reutter and Jamie Vicary · 2018
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Genuine quantum nonlocality in the triangle network
Marc-Olivier Renou, Elisa Bäumer, Sadra Boreiri, Nicolas Brunner, Nicolas Gisin, and Salman Beigi · 2019
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Quantum causal models
Jonathan Barrett, Robin Lorenz, and Ognyan Oreshkov · 2019
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Categories for Quantum Theory: an introduction
Chris Heunen and Jamie Vicary · 2019
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A quantum cellular automaton for one-dimensional qed
Pablo Arrighi, Cédric Bény, and Terry Farrelly · 2020
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Cellular automata in operational probabilistic theories
Paolo Perinotti · 2020
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Routed quantum circuits
Augustin Vanrietvelde, Hlér Kristjánsson, and Jonathan Barrett · 2020
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