Room 117

Indefinite causal structure -- a quantum outlook

Manik Banik

IMSc

The usual perception of the physical world relies on the notion
that events are ordered with respect to some global time
parameter. The standard formulation of quantum theory, like
Newtonian physics, assumes such a global order. In the recent
past, L. Hardy has initiated one possible approach to formulate
the theory of quantum gravity which should be a probabilistic
theory equipped with a dynamic space-time structure [(1) L.
Hardy, ``Towards quantum gravity: a framework for probabilistic
theories with non-fixed causal structure", J. Phys. A: Math.
Gen. 40, 3081?3099 (2007); (2) L. Hardy, ``Operational general
relativity: Possibilistic, probabilistic, and quantum",
arXiv:1608.06940]. During the recent time it has generated a lot
of research interests. Different independent formalisms have
been proposed by different research groups to
address this question. Chiribella et al. have introduced the comb
formalism to describe causally ordered quantum networks which has been
further generalized beyond causally ordered networks [ (1) G. Chiribella,
G. M. D?Ariano, P. Perinotti, and B. Valiron, ``Quantum computations
without definite causal structure", Phys.Rev. A 88, 022318 (2013)]. On the
other hand, Oreshkov et al. have introduced process matrix formalism that
ncorporates indefinite causal correlations [(1) O. Oreshkov, F. Costa, and
C. Brukner, ``Quantum correlations with no causal order", Nat. Commun. 3,
1092 (2012); (2) C. Brukner, ``Quantum causality", Nature Phys. Insight
10(4), 259 - 263 (2014)]. Interesting applications, as well as
experiments, have also been reported in the recent past [(1) G.
Chiribella, ``Perfect
discrimination of no-signalling channels via quantum superposition of causal
structures", Phys. Rev. A 86, 040301 (2012); (2) M. Araujo, F. Costa, and
C. Brukner, ``Computational advantage of quantum-controlled ordering of
gates", Phys. Rev. Lett. 113, 250402 (2014); (3) O. Oreshkov and N.
J. Cerf, ``Operational formulation of time reversal in quantum theory",
Nature Phys. (2015); (4) G. Rubino et al. ``Experimental verification of
an indefinite causal order", Science Advances (DOI:
10.1126/sciadv.1602589); (5) L. M. Procopio et al. ``Experimental
superposition of orders of quantum gates", Nat. Commun. 6, 7913 (2015)].
In my first talk, I will discuss about the process matrix formalism of
Oreshkov
et al. [Nat. Commun. 3, 1092 (2012)]. Then my plan is to talk about the
formalism of Chiribella et al. [Phys.Rev. A 88, 022318 (2013)], and
finally about the applications [Phys. Rev. A 86, 040301 (2012); Phys. Rev.
Lett.113, 250402 (2014)].