EPSRC Centre for Doctoral Training in Deliver-
ing Quantum Technologies. LM is supported by
the EPSRC.
References
[1] David Deutsch. Quantum theory of proba-
bility and decisions. Proceedings of the Royal
Society of London A: Mathematical, Physical
and Engineering Sciences. 455, 3129-3137.
1999.
[2] Wojciech Hubert Zurek. Probabilities from
entanglement, born’s rule p
k
= | ψ
k
|
2
from
envariance. Phys. Rev. A. 71, 052105. May
2005.
[3] David Wallace. How to Prove the Born Rule.
In Adrian Kent Simon Saunders, Jon Barrett
and David Wallace, editors, Many Worlds?
Everett, Quantum Theory, and Reality. Ox-
ford University Press. 2010.
[4] Markus P. Müller and Cozmin Ududec.
Structure of reversible computation deter-
mines the self-duality of quantum theory.
Phys. Rev. Lett.. 108, 130401. Mar 2012.
[5] David Gross, Markus Müller, Roger Colbeck,
and Oscar C. O. Dahlsten. All reversible dy-
namics in maximally nonlocal theories are
trivial. Phys. Rev. Lett.. 104, 080402. Feb
2010.
[6] Sabri W Al-Safi and Anthony J Short. Re-
versible dynamics in strongly non-local box-
world systems. Journal of Physics A: Math-
ematical and Theoretical. 47, 325303. 2014.
[7] Sabri W Al-Safi and Jonathan Richens. Re-
versibility and the structure of the local state
space. New Journal of Physics. 17, 123001.
2015.
[8] L. Hardy and W. K. Wootters. Lim-
ited Holism and Real-Vector-Space Quan-
tum Theory. Foundations of Physics. 42,
454-473. March 2012.
[9] D. Finkelstein, J.M. Jauch, and D. Speiser.
Notes on Quaternion Quantum Mechanics.
CERN publications: European Organization
for Nuclear Research. CERN. 1959.
[10] H. Barnum, M. Graydon, and A. Wilce.
Composites and Categories of Euclidean
Jordan Algebras. eprint ArXiv:1606.09331
quant-ph. June 2016.
[11] Scott Aaronson. Is Quantum Mechanics An
Island In Theoryspace? eprint arXiv:quant-
ph/0401062. 2004.
[12] Y. D. Han and T. Choi. Quantum Probabil-
ity assignment limited by relativistic causal-
ity. Sci. Rep.. 6, 22986. July 2016.
[13] L. Hardy. Quantum theory from five
reasonable axioms. eprint arXiv:quant-
ph/0101012. January 2001.
[14] Jonathan Barrett. Information processing in
generalized probabilistic theories. Phys. Rev.
A. 75, 032304. March 2007.
[15] Lluís Masanes and Markus P. Muller. A
derivation of quantum theory from physical
requirements. New Journal of Physics. 13,
063001. 2011.
[16] C. Brukner B. Dakic. Quantum Theory
and Beyond: Is Entanglement Special? In
H. Halvorson, editor, Deep Beauty - Under-
standing the Quantum World through Math-
ematical Innovation. pages 365–392. Cam-
bridge University Press. 2011.
[17] Robin Giles. Foundations for Quantum Me-
chanics. Journal of Mathematical Physics.
11, 2139. 1970.
[18] Bogdan Mielnik. Generalized quantum me-
chanics. Communications in Mathematical
Physics. 37, 221–256. 1974.
[19] G. Chiribella, G. M. D’Ariano, and
P. Perinotti. Probabilistic theories with pu-
rification. Physical Review A. 81, 062348.
jun 2010.
[20] H. Barnum, J. Barrett, L. Orloff Clark,
M. Leifer, R. Spekkens, N. Stepanik,
A. Wilce, and R. Wilke. Entropy and infor-
mation causality in general probabilistic the-
ories. New Journal of Physics. 12, 033024.
mar 2010.
[21] Peter Janotta and Raymond Lal. General-
ized probabilistic theories without the no-
restriction hypothesis. Physical Review A.
87, 052131. 2013.
[22] William Fulton and Joe Harris. Representa-
tion theory : a first course. Graduate texts
in mathematics. Springer-Verlag. New York,
Berlin, Paris. 1991.
[23] Jonathan Barrett. private communication.
[24] Andrew J P Garner, Oscar C O Dahlsten,
Yoshifumi Nakata, Mio Murao, and Vlatko
Vedral. A framework for phase and inter-
ference in generalized probabilistic theories.
New Journal of Physics. 15, 093044. 2013.
10