29,607 research outputs found
Device-independent tests of quantum measurements
We consider the problem of characterizing the set of input-output
correlations that can be generated by an arbitrarily given quantum measurement.
Our main result is to provide a closed-form, full characterization of such a
set for any qubit measurement, and to discuss its geometrical interpretation.
As applications, we further specify our results to the cases of real and
complex symmetric, informationally complete measurements and mutually unbiased
bases of a qubit, in the presence of isotropic noise. Our results provide the
optimal device-independent tests of quantum measurements.Comment: 5 + 2 pages, no figure
Quantum leakage detection using a model-independent dimension witness
Users of quantum computers must be able to confirm they are indeed
functioning as intended, even when the devices are remotely accessed. In
particular, if the Hilbert space dimension of the components are not as
advertised -- for instance if the qubits suffer leakage -- errors can ensue and
protocols may be rendered insecure. We refine the method of delayed vectors,
adapted from classical chaos theory to quantum systems, and apply it remotely
on the IBMQ platform -- a quantum computer composed of transmon qubits. The
method witnesses, in a model-independent fashion, dynamical signatures of
higher-dimensional processes. We present evidence, under mild assumptions, that
the IBMQ transmons suffer state leakage, with a value no larger than
under a single qubit operation. We also estimate the number
of shots necessary for revealing leakage in a two-qubit system.Comment: 11 pages, 5 figure
The Quantum PCP Conjecture
The classical PCP theorem is arguably the most important achievement of
classical complexity theory in the past quarter century. In recent years,
researchers in quantum computational complexity have tried to identify
approaches and develop tools that address the question: does a quantum version
of the PCP theorem hold? The story of this study starts with classical
complexity and takes unexpected turns providing fascinating vistas on the
foundations of quantum mechanics, the global nature of entanglement and its
topological properties, quantum error correction, information theory, and much
more; it raises questions that touch upon some of the most fundamental issues
at the heart of our understanding of quantum mechanics. At this point, the jury
is still out as to whether or not such a theorem holds. This survey aims to
provide a snapshot of the status in this ongoing story, tailored to a general
theory-of-CS audience.Comment: 45 pages, 4 figures, an enhanced version of the SIGACT guest column
from Volume 44 Issue 2, June 201
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