6 research outputs found
Routed quantum circuits: an extended framework for coherent control and indefinite causal order
Quantum circuits form the standard framework of quantum computing, and have started playing the same role for some parts of quantum foundations. However, they cannot satisfactorily capture some possibilities offered by quantum theory, in particular coherent control and indefinite causal order. In this thesis, we therefore propose an extension to this framework, given by routed quantum circuits. Our extension is based on the addition of sectorial constraints, which specify the basic sectorial structure of the scenarios at hand, on top of the factorial structure described by the connectivity of circuits. This yields a consistent and scalable framework, applicable to pure and mixed quantum theory. It admits a sound and intuitive diagrammatic notation.
We show that this framework allows to properly model all forms of coherent control of the application of a channel, for instance the superposition of a quantum information carrier's trajectory, or the 'extended circuit diagrams' recently introduced for the study of causal decompositions. We demonstrate how this leads to a redefinition of the task of coherently controlling a channel, and study in detail the necessary resources for this task. We further show that the scenarios featuring indefinite causal order also fit within our framework once feedback loops are introduced. The connectivity and sectorial constraints are then sufficient to specify the core behaviour of a process, and in particular to check that it is valid, i.e. that its cycles do not lead to any logical inconsistency. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes.Open Acces
Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
Given the importance of quantum reference systems to both quantum and
gravitational physics, it is pertinent to develop a systematic method for
switching between the descriptions of physics relative to different choices of
quantum reference systems, which is valid in both fields. Here, we continue
with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients
is a gravity-inspired symmetry principle, which enforces physics to be
relational and leads, thanks to gauge related redundancies, to a
perspective-neutral structure which contains all frame choices at once and via
which frame perspectives can be consistently switched. Formulated in the
language of constrained systems, the perspective-neutral structure turns out to
be the constraint surface classically and the gauge invariant Hilbert space in
the Dirac quantized theory. By contrast, a perspective relative to a specific
frame corresponds to a gauge choice and the associated reduced phase and
Hilbert space. Quantum reference frame switches thereby amount to a symmetry
transformation. In the quantum theory, they require a transformation that takes
one from the Dirac to a reduced quantum theory and we show that it amounts to a
trivialization of the constraints and a subsequent projection onto the
classical gauge fixing conditions. We illustrate this method in the relational
-body problem with rotational and translational symmetry. This model is
particularly interesting because it features the Gribov problem so that
globally valid gauge fixing conditions are impossible which, in turn, implies
also that globally valid relational frame perspectives are absent in both the
classical and quantum theory. These challenges notwithstanding, we exhibit how
one can systematically construct the quantum reference frame transformations
for the three-body problem.Comment: 22 pages, plus appendice
Causal structure in the presence of sectorial constraints, with application to the quantum switch
Existing work on quantum causal structure assumes that one can perform
arbitrary operations on the systems of interest. But this condition is often
not met. Here, we extend the framework for quantum causal modelling to cases
where a system can suffer \textit{sectorial contraints}, that is, restrictions
on the orthogonal subspaces of its Hilbert space that may be mapped to one
another. Our framework (a) proves that a number of different intuitions about
causal relations turn out to be equivalent; (b) shows that quantum causal
structures in the presence of sectorial constraints can be represented with a
directed graph; and (c) defines a fine-graining of the causal structure in
which the individual sectors of a system bear causal relations, which provides
a more detailed analysis than its coarse-grained counterpart. As an example, we
apply our framework to purported photonic implementations of the quantum switch
to show that while their coarse-grained causal structure is cyclic, their
fine-grained causal structure is acyclic. We therefore conclude that these
experiments realize indefinite causal order only in a weak sense. Notably, this
is the first argument to this effect that is not rooted in the assumption that
the causal relata must be localized in spacetime
Routed quantum circuits
We argue that the quantum-theoretical structures studied in several recent
lines of research cannot be adequately described within the standard framework
of quantum circuits. This is in particular the case whenever the combination of
subsystems is described by a nontrivial blend of direct sums and tensor
products of Hilbert spaces. We therefore propose an extension to the framework
of quantum circuits, given by \textit{routed linear maps} and \textit{routed
quantum circuits}. We prove that this new framework allows for a consistent and
intuitive diagrammatic representation in terms of circuit diagrams, applicable
to both pure and mixed quantum theory, and exemplify its use in several
situations, including the superposition of quantum channels and the causal
decompositions of unitaries. We show that our framework encompasses the
`extended circuit diagrams' of Lorenz and Barrett [arXiv:2001.07774 (2020)],
which we derive as a special case, endowing them with a sound semantics.Comment: 21 pages + appendix. Comments welcom