570 research outputs found
Assessments of macroscopicity for quantum optical states
With the slow but constant progress in the coherent control of quantum
systems, it is now possible to create large quantum superpositions. There has
therefore been an increased interest in quantifying any claims of
macroscopicity. We attempt here to motivate three criteria which we believe
should enter in the assessment of macroscopic quantumness: The number of
quantum fluctuation photons, the purity of the states, and the ease with which
the branches making up the state can be distinguished
Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
We analyze quantum states formed as superpositions of an initial pure product
state and its image under local unitary evolution, using two measurement-based
measures of superposition size: one based on the optimal quantum binary
distinguishability of the branches of the superposition and another based on
the ratio of the maximal quantum Fisher information of the superposition to
that of its branches, i.e., the relative metrological usefulness of the
superposition. A general formula for the effective sizes of these states
according to the branch distinguishability measure is obtained and applied to
superposition states of quantum harmonic oscillators composed of Gaussian
branches. Considering optimal distinguishability of pure states on a
time-evolution path leads naturally to a notion of distinguishability time that
generalizes the well known orthogonalization times of Mandelstam and Tamm and
Margolus and Levitin. We further show that the distinguishability time provides
a compact operational expression for the superposition size measure based on
the relative quantum Fisher information. By restricting the maximization
procedure in the definition of this measure to an appropriate algebra of
observables, we show that the superposition size of, e.g., N00N states and
hierarchical cat states, can scale linearly with the number of elementary
particles comprising the superposition state, implying precision scaling
inversely with the total number of photons when these states are employed as
probes in quantum parameter estimation of a 1-local Hamiltonian in this
algebra
Resource theory of asymmetric distinguishability
This paper systematically develops the resource theory of asymmetric
distinguishability, as initiated roughly a decade ago [K. Matsumoto,
arXiv:1010.1030 (2010)]. The key constituents of this resource theory are
quantum boxes, consisting of a pair of quantum states, which can be manipulated
for free by means of an arbitrary quantum channel. We introduce bits of
asymmetric distinguishability as the basic currency in this resource theory,
and we prove that it is a reversible resource theory in the asymptotic limit,
with the quantum relative entropy being the fundamental rate of resource
interconversion. The distillable distinguishability is the optimal rate at
which a quantum box consisting of independent and identically distributed
(i.i.d.) states can be converted to bits of asymmetric distinguishability, and
the distinguishability cost is the optimal rate for the reverse transformation.
Both of these quantities are equal to the quantum relative entropy. The exact
one-shot distillable distinguishability is equal to the min-relative entropy,
and the exact one-shot distinguishability cost is equal to the max-relative
entropy. Generalizing these results, the approximate one-shot distillable
distinguishability is equal to the smooth min-relative entropy, and the
approximate one-shot distinguishability cost is equal to the smooth
max-relative entropy. As a notable application of the former results, we prove
that the optimal rate of asymptotic conversion from a pair of i.i.d. quantum
states to another pair of i.i.d. quantum states is fully characterized by the
ratio of their quantum relative entropies.Comment: v3: 28 page
Entropic measures of joint uncertainty: effects of lack of majorization
We compute R\'enyi entropies for the statistics of a noisy simultaneous
observation of two complementary observables in two-dimensional quantum
systems. The relative amount of uncertainty between two states depends on the
uncertainty measure used. These results are not reproduced by a more standard
duality relation. We show that these behaviors are consistent with the lack of
majorization relation between the corresponding statistics.Comment: 10 pages, 3 figure
Comparison of non-Markovianity criteria in a qubit system under random external fields
We give the map representing the evolution of a qubit under the action of
non-dissipative random external fields. From this map we construct the
corresponding master equation that in turn allows us to phenomenologically
introduce population damping of the qubit system. We then compare, in this
system, the time-regions when non-Markovianity is present on the basis of
different criteria both for the non-dissipative and dissipative case. We show
that the adopted criteria agree both in the non-dissipative case and in the
presence of population damping.Comment: 8 pages, 1 figure. Some changes made. In press on Physica Scripta T
(special issue
Geometry from Information Geometry
We use the method of maximum entropy to model physical space as a curved
statistical manifold. It is then natural to use information geometry to explain
the geometry of space. We find that the resultant information metric does not
describe the full geometry of space but only its conformal geometry -- the
geometry up to local changes of scale. Remarkably, this is precisely what is
needed to model "physical" space in general relativity.Comment: Presented at MaxEnt 2015, the 35th International Workshop on Bayesian
Inference and Maximum Entropy Methods in Science and Engineering (July 19-24,
2015, Potsdam NY, USA
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