79 research outputs found
SU(N)-symmetric quasi-probability distribution functions
We present a set of N-dimensional functions, based on generalized
SU(N)-symmetric coherent states, that represent finite-dimensional Wigner
functions, Q-functions, and P-functions. We then show the fundamental
properties of these functions and discuss their usefulness for analyzing
N-dimensional pure and mixed quantum states.Comment: 16 pages, 2 figures. Updated text to reflect referee comment
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
Hilbert--Schmidt volume of the set of mixed quantum states
We compute the volume of the convex N^2-1 dimensional set M_N of density
matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area
of the boundary of this set is also found and its ratio to the volume provides
an information about the complex structure of M_N. Similar investigations are
also performed for the smaller set of all real density matrices. As an
intermediate step we analyze volumes of the unitary and orthogonal groups and
of the flag manifolds.Comment: 13 revtex pages, ver 3: minor improvement
SU(N) Coherent States and Irreducible Schwinger Bosons
We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent
states. This construction of SU(N) coherent state is analogous to the
construction of the simplest Heisenberg-Weyl coherent states. The coherent
states belonging to irreducible representations of SU(N) are labeled by the
eigenvalues of the SU(N) Casimir operators and are characterized by
complex orthonormal vectors describing the SU(N) group manifold.Comment: 12 pages, 3 figure
A priori probability that a qubit-qutrit pair is separable
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact
computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures
volume of mixed quantum states" to refine our conjecture
Bures volume of the set of mixed quantum states
We compute the volume of the N^2-1 dimensional set M_N of density matrices of
size N with respect to the Bures measure and show that it is equal to that of a
N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume
of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the
boundary of the set M_N and obtain analogous results for the smaller set of all
real density matrices. An explicit formula for the Bures-Hall normalization
constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte
A Parametrization of Bipartite Systems Based on SU(4) Euler Angles
In this paper we give an explicit parametrization for all two qubit density
matrices. This is important for calculations involving entanglement and many
other types of quantum information processing. To accomplish this we present a
generalized Euler angle parametrization for SU(4) and all possible two qubit
density matrices. The important group-theoretical properties of such a
description are then manifest. We thus obtain the correct Haar (Hurwitz)
measure and volume element for SU(4) which follows from this parametrization.
In addition, we study the role of this parametrization in the Peres-Horodecki
criteria for separability and its corresponding usefulness in calculating
entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain
areas in line with referee comments. To be published in J. Phys. A: Math. and
Ge
Impact of cumulative body mass index and cardiometabolic diseases on survival among patients with colorectal and breast cancer: a multi-centre cohort study
BACKGROUND: Body mass index (BMI) and cardiometabolic comorbidities such as cardiovascular disease and type 2 diabetes have been studied as negative prognostic factors in cancer survival, but possible dependencies in the mechanisms underlying these associations remain largely unexplored. We analysed these associations in colorectal and breast cancer patients. METHODS: Based on repeated BMI assessments of cancer-free participants from four European countries in the European Prospective Investigation into Cancer and nutrition (EPIC) study, individual BMI-trajectories reflecting predicted mean BMI between ages 20 to 50 years were estimated using a growth curve model. Participants with incident colorectal or breast cancer after the age of 50 years were included in the survival analysis to study the prognostic effect of mean BMI and cardiometabolic diseases (CMD) prior to cancer. CMD were defined as one or more chronic conditions among stroke, myocardial infarction, and type 2 diabetes. Hazard ratios (HRs) and confidence intervals (CIs) of mean BMI and CMD were derived using multivariable-adjusted Cox proportional hazard regression for mean BMI and CMD separately and both exposures combined, in subgroups of localised and advanced disease. RESULTS: In the total cohort of 159,045 participants, there were 1,045 and 1,620 eligible patients of colorectal and breast cancer. In colorectal cancer patients, a higher BMI (by 1 kg/m2) was associated with a 6% increase in risk of death (95% CI of HR: 1.02-1.10). The HR for CMD was 1.25 (95% CI: 0.97-1.61). The associations for both exposures were stronger in patients with localised colorectal cancer. In breast cancer patients, a higher BMI was associated with a 4% increase in risk of death (95% CI: 1.00-1.08). CMDs were associated with a 46% increase in risk of death (95% CI: 1.01-2.09). The estimates and CIs for BMI remained similar after adjustment for CMD and vice versa. CONCLUSIONS: Our results suggest that cumulative exposure to higher BMI during early to mid-adulthood was associated with poorer survival in patients with breast and colorectal cancer, independent of CMD prior to cancer diagnosis. The association between a CMD diagnosis prior to cancer and survival in patients with breast and colorectal cancer was independent of BMI
Advances in quantum metrology
The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections
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