14,774 research outputs found
Maximum stabilizer dimension for nonproduct states
Composite quantum states can be classified by how they behave under local
unitary transformations. Each quantum state has a stabilizer subgroup and a
corresponding Lie algebra, the structure of which is a local unitary invariant.
In this paper, we study the structure of the stabilizer subalgebra for n-qubit
pure states, and find its maximum dimension to be n-1 for nonproduct states of
three qubits and higher. The n-qubit Greenberger-Horne-Zeilinger state has a
stabilizer subalgebra that achieves the maximum possible dimension for pure
nonproduct states. The converse, however, is not true: we show examples of pure
4-qubit states that achieve the maximum nonproduct stabilizer dimension, but
have stabilizer subalgebra structures different from that of the n-qubit GHZ
state.Comment: 6 page
Werner state structure and entanglement classification
We present applications of the representation theory of Lie groups to the
analysis of structure and local unitary classification of Werner states,
sometimes called the {\em decoherence-free} states, which are states of
quantum bits left unchanged by local transformations that are the same on each
particle. We introduce a multiqubit generalization of the singlet state, and a
construction that assembles these into Werner states.Comment: 9 pages, 2 figures, minor changes and corrections for version
Classification of nonproduct states with maximum stabilizer dimension
Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups
of the group of local unitary transformations are precisely the generalized
n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents,
for n greater than or equal to 3 but not equal to 4. We characterize the Lie
algebra of the stabilizer subgroup for these states. For n=4, there is an
additional maximal stabilizer subalgebra, not local unitary equivalent to the
former. We give a canonical form for states with this stabilizer as well.Comment: 6 pages, version 3 has a typographical correction in the displayed
equation just after numbered equation (2), and other minor correction
Minimum orbit dimension for local unitary action on n-qubit pure states
The group of local unitary transformations partitions the space of n-qubit
quantum states into orbits, each of which is a differentiable manifold of some
dimension. We prove that all orbits of the n-qubit quantum state space have
dimension greater than or equal to 3n/2 for n even and greater than or equal to
(3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since
n-qubit states composed of products of singlets achieve these lowest orbit
dimensions.Comment: 19 page
Classification of n-qubit states with minimum orbit dimension
The group of local unitary transformations acts on the space of n-qubit pure
states, decomposing it into orbits. In a previous paper we proved that a
product of singlet states (together with an unentangled qubit for a system with
an odd number of qubits) achieves the smallest possible orbit dimension, equal
to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits.
In this paper we show that any state with minimum orbit dimension must be of
this form, and furthermore, such states are classified up to local unitary
equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene
Microwave properties of DyBa_2Cu_3O_(7-x) monodomains and related compounds in magnetic fields
We present a microwave characterization of a DyBaCuO
single domain, grown by the top-seeded melt-textured technique. We report the
(a,b) plane field-induced surface resistance, , at 48.3 GHz,
measured by means of a cylindrical metal cavity in the end-wall-replacement
configuration. Changes in the cavity quality factor Q against the applied
magnetic field yield at fixed temperatures. The temperature
range [70 K ; T_c] was explored. The magnetic field 0.8 T was
applied along the c axis. The field dependence of does not
exhibit the steep, step-like increase at low fields typical of weak-links. This
result indicates the single-domain character of the sample under investigation.
exhibits a nearly square-root dependence on H, as expected for
fluxon motion. From the analysis of the data in terms of motion of Abrikosov
vortices we estimate the temperature dependences of the London penetration
depth and the vortex viscosity , and their zero-temperature
values 165 nm and 3 10 Nsm, which are
found in excellent agreement with reported data in YBaCuO
single crystals. Comparison of microwave properties with those of related
samples indicate the need for reporting data as a function of T/T_c in order to
obtain universal laws.Comment: 6 pages, 4 figures, LaTeX, submitted to Journal of Applied Physic
It takes one to know one: Relationship between lie detection and psychopathy
We investigated primary and secondary psychopathy and the ability to detect high-stakes, real-life emotional lies in an on-line experiment (N = 150). Using signal detection analysis, we found that lie detection ability was overall above chance level, there was a tendency towards responding liberally to the test stimuli, and women were more accurate than men Further, sex moderated the relationship between psychopathy and lie detection ability; in men, primary psychopathy had a significant positive correlation with the ability to detect lies, whereas in women there was a significant negative correlation with deception detection. The results are discussed with reference to evolutionary theory and sex differences in processing socio-emotional information
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II
The strong convergence of Wong-Zakai approximations of the solution to the
reflecting stochastic differential equations was studied in [2]. We continue
the study and prove the strong convergence under weaker assumptions on the
domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of
Terry Lyons", Springer Proceedings in Mathematics and Statistic
Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
We classify, up to local unitary equivalence, the set of -qubit states
that is stabilized by the diagonal subgroup of the local unitary group. We
exhibit a basis for this set, parameterized by diagrams of nonintersecting
chords connecting pairs of points on a circle, and give a criterion for when
the stabilizer is precisely the diagonal subgroup and not larger. This
investigation is part of a larger program to partially classify entanglement
type (local unitary equivalence class) via analysis of stabilizer structure.Comment: 4 pages, 3 figures. Version 2 has numerous small changes and
correction
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