67 research outputs found
Reconstruction of superoperators from incomplete measurements
We present strategies how to reconstruct (estimate) properties of a quantum
channel described by the map E based on incomplete measurements. In a
particular case of a qubit channel a complete reconstruction of the map E can
be performed via complete tomography of four output states E[rho_j ] that
originate from a set of four linearly independent test states j (j = 1, 2, 3,
4) at the input of the channel. We study the situation when less than four
linearly independent states are transmitted via the channel and measured at the
output. We present strategies how to reconstruct the channel when just one, two
or three states are transmitted via the channel. In particular, we show that if
just one state is transmitted via the channel then the best reconstruction can
be achieved when this state is a total mixture described by the density
operator rho = I/2. To improve the reconstruction procedure one has to send via
the channel more states. The best strategy is to complement the total mixture
with pure states that are mutually orthogonal in the sense of the Bloch-sphere
representation. We show that unitary transformations (channels) can be uniquely
reconstructed (determined) based on the information of how three properly
chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure
Transition Probability (Fidelity) and Its Relatives
Transition Probability (fidelity) for pairs of density operators can be
defined as "functor" in the hierarchy of "all" quantum systems and also within
any quantum system. The introduction of "amplitudes" for density operators
allows for a more intuitive treatment of these quantities, also pointing to a
natural parallel transport. The latter is governed by a remarkable gauge theory
with strong relations to the Riemann-Bures metric.Comment: Talk at the 2009 Vaexoe Quantum Theory Conference. 11 page
Kakutani Dichotomy on Free States
Two quasi-free states on a CAR or CCR algebra are shown to generate
quasi-equivalent representations unless they are disjoint.Comment: 12 page
Continuity of the von Neumann entropy
A general method for proving continuity of the von Neumann entropy on subsets
of positive trace-class operators is considered. This makes it possible to
re-derive the known conditions for continuity of the entropy in more general
forms and to obtain several new conditions. The method is based on a particular
approximation of the von Neumann entropy by an increasing sequence of concave
continuous unitary invariant functions defined using decompositions into finite
rank operators. The existence of this approximation is a corollary of a general
property of the set of quantum states as a convex topological space called the
strong stability property. This is considered in the first part of the paper.Comment: 42 pages, the minor changes have been made, the new applications of
the continuity condition have been added. To appear in Commun. Math. Phy
Partitioned trace distances
New quantum distance is introduced as a half-sum of several singular values
of difference between two density operators. This is, up to factor, the metric
induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar
properties to the standard trace distance, including the unitary invariance,
the strong convexity and the close relations to the classical distances. The
partitioned distances cannot increase under quantum operations of certain kind
including bistochastic maps. All the basic properties are re-formulated as
majorization relations. Possible applications to quantum information processing
are briefly discussed.Comment: 8 pages, no figures. Significant changes are made. New section on
majorization is added. Theorem 4.1 is extended. The bibliography is enlarged
Quantum hypothesis testing and sufficient subalgebras
We introduce a new notion of a sufficient subalgebra for quantum states: a
subalgebra is 2- sufficient for a pair of states if it
contains all Bayes optimal tests of against . In classical
statistics, this corresponds to the usual definition of sufficiency. We show
this correspondence in the quantum setting for some special cases. Furthermore,
we show that sufficiency is equivalent to 2 - sufficiency, if the latter is
required for , for all .Comment: 12 page
Quantum Iterated Function Systems
Iterated functions system (IFS) is defined by specifying a set of functions
in a classical phase space, which act randomly on an initial point. In an
analogous way, we define a quantum iterated functions system (QIFS), where
functions act randomly with prescribed probabilities in the Hilbert space. In a
more general setting a QIFS consists of completely positive maps acting in the
space of density operators. We present exemplary classical IFSs, the invariant
measure of which exhibits fractal structure, and study properties of the
corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include
Assessment of plasma chitotriosidase activity, CCL18/PARC concentration and NP-C suspicion index in the diagnosis of Niemann-Pick disease type C: A prospective observational study
Background: Niemann-Pick disease type C (NP-C) is a rare, autosomal recessive neurodegenerative disease caused by mutations in either the NPC1 or NPC2 genes. The diagnosis of NP-C remains challenging due to the non-specific, heterogeneous nature of signs/symptoms. This study assessed the utility of plasma chitotriosidase (ChT) and Chemokine (C-C motif) ligand 18 (CCL18)/pulmonary and activation-regulated chemokine (PARC) in conjunction with the NP-C suspicion index (NP-C SI) for guiding confirmatory laboratory testing in patients with suspected NP-C. Methods: In a prospective observational cohort study, incorporating a retrospective determination of NP-C SI scores, two different diagnostic approaches were applied in two separate groups of unrelated patients from 51 Spanish medical centers (n = 118 in both groups). From Jan 2010 to Apr 2012 (Period 1), patients with =2 clinical signs/symptoms of NP-C were considered ''suspected NP-C'' cases, and NPC1/NPC2 sequencing, plasma chitotriosidase (ChT), CCL18/PARC and sphingomyelinase levels were assessed. Based on findings in Period 1, plasma ChT and CCL18/PARC, and NP-C SI prediction scores were determined in a second group of patients between May 2012 and Apr 2014 (Period 2), and NPC1 and NPC2 were sequenced only in those with elevated ChT and/or elevated CCL18/PARC and/or NP-C SI =70. Filipin staining and 7-ketocholesterol (7-KC) measurements were performed in all patients with NP-C gene mutations, where possible. Results: In total across Periods 1 and 2, 10/236 (4%) patients had a confirmed diagnosis o NP-C based on gene sequencing (5/118 4.2%] in each Period): all of these patients had two causal NPC1 mutations. Single mutant NPC1 alleles were detected in 8/236 (3%) patients, overall. Positive filipin staining results comprised three classical and five variant biochemical phenotypes. No NPC2 mutations were detected. All patients with NPC1 mutations had high ChT activity, high CCL18/PARC concentrations and/or NP-C SI scores =70. Plasma 7-KC was higher than control cut-off values in all patients with two NPC1 mutations, and in the majority of patients with single mutations. Family studies identified three further NP-C patients. Conclusion: This approach may be very useful for laboratories that do not have mass spectrometry facilities and therefore, they cannot use other NP-C biomarkers for diagnosis
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