198 research outputs found
Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
For both unitary and open qubit dynamics, we compare asymmetry monotone-based
bounds on the minimal time required for an initial qubit state to evolve to a
final qubit state from which it is probabilistically distinguishable with fixed
minimal error probability (i.e., the minimal error distinguishability time).
For the case of unitary dynamics generated by a time-independent Hamiltonian,
we derive a necessary and sufficient condition on two asymmetry monotones that
guarantees that an arbitrary state of a two-level quantum system or a separable
state of two-level quantum systems will unitarily evolve to another state
from which it can be distinguished with a fixed minimal error probability
. This condition is used to order the set of qubit states
based on their distinguishability time, and to derive an optimal release time
for driven two-level systems such as those that occur, e.g., in the
Landau-Zener problem. For the case of non-unitary dynamics, we compare three
lower bounds to the distinguishability time, including a new type of lower
bound which is formulated in terms of the asymmetry of the uniformly
time-twirled initial system-plus-environment state with respect to the
generator of the Stinespring isometry corresponding to the dynamics,
specifically, in terms of ,
where .Comment: 13 pages, 4 figure
Quantum Approximation of Normalized Schatten Norms and Applications to Learning
Efficient measures to determine similarity of quantum states, such as the
fidelity metric, have been widely studied. In this paper, we address the
problem of defining a similarity measure for quantum operations that can be
\textit{efficiently estimated}. Given two quantum operations, and ,
represented in their circuit forms, we first develop a quantum sampling circuit
to estimate the normalized Schatten 2-norm of their difference () with precision , using only one clean qubit and one
classical random variable. We prove a Poly upper bound on
the sample complexity, which is independent of the size of the quantum system.
We then show that such a similarity metric is directly related to a functional
definition of similarity of unitary operations using the conventional fidelity
metric of quantum states (): If is sufficiently small
(e.g. ) then the fidelity of
states obtained by processing the same randomly and uniformly picked pure
state, , is as high as needed () with probability exceeding . We
provide example applications of this efficient similarity metric estimation
framework to quantum circuit learning tasks, such as finding the square root of
a given unitary operation.Comment: 25 pages, 4 figures, 6 tables, 1 algorith
Entanglement, intractability and no-signaling
We consider the problem of deriving the no-signaling condition from the
assumption that, as seen from a complexity theoretic perspective, the universe
is not an exponential place. A fact that disallows such a derivation is the
existence of {\em polynomial superluminal} gates, hypothetical primitive
operations that enable superluminal signaling but not the efficient solution of
intractable problems. It therefore follows, if this assumption is a basic
principle of physics, either that it must be supplemented with additional
assumptions to prohibit such gates, or, improbably, that no-signaling is not a
universal condition. Yet, a gate of this kind is possibly implicit, though not
recognized as such, in a decade-old quantum optical experiment involving
position-momentum entangled photons. Here we describe a feasible modified
version of the experiment that appears to explicitly demonstrate the action of
this gate. Some obvious counter-claims are shown to be invalid. We believe that
the unexpected possibility of polynomial superluminal operations arises because
some practically measured quantum optical quantities are not describable as
standard quantum mechanical observables.Comment: 17 pages, 2 figures (REVTeX 4
Implementing generalized measurements with superconducting qubits
We describe a method to perform any generalized purity-preserving measurement
of a qubit with techniques tailored to superconducting systems. First, we
consider two methods for realizing a two-outcome partial projection: using a
thresholded continuous measurement in the circuit QED setup, or using an
indirect ancilla qubit measurement. Second, we decompose an arbitrary
purity-preserving two-outcome measurement into single qubit unitary rotations
and a partial projection. Third, we systematically reduce any multiple-outcome
measurement to a sequence of such two-outcome measurements and unitary
operations. Finally, we consider how to define suitable fidelity measures for
multiple-outcome generalized measurements.Comment: 13 pages, 3 figure
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