408 research outputs found
Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
A bosonic state is commonly considered nonclassical (or quantum) if its
Glauber-Sudarshan function is not a classical probability density, which
implies that only coherent states and their statistical mixtures are classical.
We quantify the nonclassicality of a single qubit, defined by the vacuum and
single-photon states, by applying the following four well-known measures of
nonclassicality: (1) the nonclassical depth, , related to the minimal
amount of Gaussian noise which changes a nonpositive function into a
positive one; (2) the nonclassical distance , defined as the Bures distance
of a given state to the closest classical state, which is the vacuum for the
single-qubit Hilbert space; together with (3) the negativity potential (NP) and
(4) concurrence potential, which are the nonclassicality measures corresponding
to the entanglement measures (i.e., the negativity and concurrence,
respectively) for the state generated by mixing a single-qubit state with the
vacuum on a balanced beam splitter. We show that complete statistical mixtures
of the vacuum and single-photon states are the most nonclassical single-qubit
states regarding the distance for a fixed value of both the depth
and NP in the whole range of their values, as well as the NP for a
given value of such that . Conversely, pure states are the
most nonclassical single-qubit states with respect to for a given ,
NP versus , and versus NP. We also show the "relativity" of these
nonclassicality measures by comparing pairs of single-qubit states: if a state
is less nonclassical than another state according to some measure then it might
be more nonclassical according to another measure. Moreover, we find that the
concurrence potential is equal to the nonclassical distance for single-qubit
states.Comment: 12 pages, 3 figures, and 3 table
Quantumness of spin-1 states
We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt
distance to the convex hull of spin coherent states. We derive its analytic
expression in the case of pure states as a function of the smallest eigenvalue
of the Bloch matrix and give explicitly the closest classical state for an
arbitrary pure state. Numerical evidence is provided that the exact formula for
pure states provides an upper bound on the quantumness of mixed states. Due to
the connection between quantumness and entanglement we obtain new insights into
the geometry of symmetric entangled states
Decoherence, einselection, and the quantum origins of the classical
Decoherence is caused by the interaction with the environment. Environment
monitors certain observables of the system, destroying interference between the
pointer states corresponding to their eigenvalues. This leads to
environment-induced superselection or einselection, a quantum process
associated with selective loss of information. Einselected pointer states are
stable. They can retain correlations with the rest of the Universe in spite of
the environment. Einselection enforces classicality by imposing an effective
ban on the vast majority of the Hilbert space, eliminating especially the
flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase
space emerges from the quantum Hilbert space in the appropriate macroscopic
limit: Combination of einselection with dynamics leads to the idealizations of
a point and of a classical trajectory. In measurements, einselection replaces
quantum entanglement between the apparatus and the measured system with the
classical correlation.Comment: Final version of the review, with brutally compressed figures. Apart
from the changes introduced in the editorial process the text is identical
with that in the Rev. Mod. Phys. July issue. Also available from
http://www.vjquantuminfo.or
Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity
We introduce a new distance-based measure for the nonclassicality of the
states of a bosonic field, which outperforms the existing such measures in
several ways. We define for that purpose the operator ordering sensitivity of
the state which evaluates the sensitivity to operator ordering of the Renyi
entropy of its quasi-probabilities and which measures the oscillations in its
Wigner function. Through a sharp control on the operator ordering sensitivity
of classical states we obtain a precise geometric image of their location in
the density matrix space allowing us to introduce a distance-based measure of
nonclassicality. We analyse the link between this nonclassicality measure and a
recently introduced quantum macroscopicity measure, showing how the two notions
are distinct
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