Multipartite quantum correlations: symplectic and algebraic geometry approach

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite number of energy levels, classification problems are usually treated in frames of linear algebra. We proposed to shift the attention to a geometric description. Treating consistently quantum states as points of a projective space rather than as vectors in a Hilbert space we were able to apply powerful methods of differential, symplectic and algebraic geometry to attack the problem of equivalence of states with respect to the strength of correlations, or, in other words, to classify them from this point of view. Such classifications are interpreted as identification of states with `the same correlations properties' i.e. ones that can be used for the same information purposes, or, from yet another point of view, states that can be mutually transformed one to another by specific, experimentally accessible operations. It is clear that the latter characterization answers the fundamental question `what can be transformed into what \textit{via} available means?'. Exactly such an interpretations, i.e, in terms of mutual transformability can be clearly formulated in terms of actions of specific groups on the space of states and is the starting point for the proposed methods.Comment: 29 pages, 9 figures, 2 tables, final form submitted to the journa

Separability in 2xN composite quantum systems

We analyze the separability properties of density operators supported on \C^2\otimes \C^N whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states have rank larger than N. We also give a separability criterion for a generic density operator such that the sum of its rank and the one of its partial transpose does not exceed 3N. If it exceeds this number we show that one can subtract product vectors until decreasing it to 3N, while keeping the positivity of $\rho$ and its partial transpose. This automatically gives us a sufficient criterion for separability for general density operators. We also prove that all density operators that remain invariant after partial transposition with respect to the first system are separable.Comment: Extended version of quant-ph/9903012 with new results. 11 page

Micelle-Encapsulated Quantum Dot-Porphyrin Assemblies as

Micelles have been employed to encapsulate the supramolecular assembly of quantum dots with palladium(II) porphyrins for the quantification of O₂ levels in aqueous media and in vivo. Förster resonance energy transfer from the quantum dot (QD) to the palladium porphyrin provides a means for signal transduction under both one- and two-photon excitation. The palladium porphyrins are sensitive to O₂ concentrations in the range of 0–160 Torr. The micelle-encapsulated QD-porphyrin assemblies have been employed for in vivo multiphoton imaging and lifetime-based oxygen measurements in mice with chronic dorsal skinfold chambers or cranial windows. Our results establish the utility of the QD-micelle approach for in vivo biological sensing applications.National Cancer Institute (U.S.) (R01- CA126642)International Society for Neurochemistry (W911NF-07-D-0004)United States. Dept. of Energy. Office of Basic Energy Sciences (DE-SC0009758

Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems

It is shown that for a given bipartite density matrix and by choosing a suitable separable set (instead of product set) on the separable-entangled boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via optimization for a generic entangled density matrix. Based on this, We obtain optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and $2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters basis, iso-concurrence decomposable states, states obtained from BD states via one parameter and three parameters local operations and classical communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one parameter $3\otimes 3$ state. We also obtain the optimal decomposition for multi partite isotropic state. It is shown that in all $2\otimes 2$ systems considered here the average concurrence of the decomposition is equal to the concurrence. We also show that for some $2\otimes 3$ Bell decomposable states the average concurrence of the decomposition is equal to the lower bound of the concurrence of state presented recently in [Buchleitner et al, quant-ph/0302144], so an exact expression for concurrence of these states is obtained. It is also shown that for $d\otimes d$ isotropic state where decomposition leads to a separable and an entangled pure state, the average I-concurrence of the decomposition is equal to the I-concurrence of the state. Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition, Concurrence, Bell decomposable states, LOCC} PACS Index: 03.65.UdComment: 31 pages, Late

Separability and entanglement in 2x3xN composite quantum systems

The separability and entanglement of quantum mixed states in \Cb^2 \otimes \Cb^3 \otimes \Cb^N composite quantum systems are investigated. It is shown that all quantum states $\rho$ with positive partial transposes and rank $r(\rho)\leq N$ are separable.Comment: Latex, 15 page

Separability and entanglement in 2x2xN composite quantum systems

We investigate separability and entanglement of mixed states in ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For the 3 qubit case (N=2) we prove that all states $\rho$ that have positive partial transposes and rank 3 are separable. We provide also constructive separability checks for the states $\rho$ that have the sum of the rank of $\rho$ and the ranks of partial transposes with respect to all subsystems smaller than 15N-1.Comment: Finally corrected file submitted. Numerous misprints and small errors corrected, better versions of constructive separability checks included, updated and extended reference

Synchrotron radiation-based experimental determination of the optimal energy for cell radiotoxicity enhancement following photoelectric effect on stable iodinated compounds

This study was designed to experimentally evaluate the optimal X-ray energy for increasing the radiation energy absorbed in tumours loaded with iodinated compounds, using the photoelectric effect. SQ20B human cells were irradiated with synchrotron monochromatic beam tuned at 32.8, 33.5, 50 and 70 keV. Two cell treatments were compared to the control: cells suspended in 10 mg ml1 of iodine radiological contrast agent or cells pre-exposed with 10 mM of iodo-desoxyuridine (IUdR) for 48 h. Our radiobiological end point was clonogenic cell survival. Cells irradiated with both iodine compounds exhibited a radiation sensitisation enhancement. Moreover, it was energy dependent, with a maximum at 50 keV. At this energy, the sensitisation calculated at 10% survival was equal to 2.03 for cells suspended in iodinated contrast agent and 2.60 for IUdR. Cells pretreated with IUdR had higher sensitisation factors over the energy range than for those suspended in iodine contrast agent. Also, their survival curves presented no shoulder, suggesting complex lethal damages from Auger electrons. Our results confirm the existence of the 50 keV energy optimum for a binary therapeutic irradiation based on the presence of stable iodine in tumours and an external irradiation. Monochromatic synchrotron radiotherapy concept is hence proposed for increasing the differential effect between healthy and cancerous tissue irradiation

Micelle-Encapsulated Quantum Dot-Porphyrin Assemblies asin VivoTwo-Photon Oxygen Sensors

Micelles have been employed to encapsulate the supramolecular assembly of quantum dots with palladium(II) porphyrins for the quantification of O2 levels in aqueous media and in vivo. Förster resonance energy transfer from the quantum dot (QD) to the palladium porphyrin provides a means for signal transduction under both one- and two-photon excitation. The palladium porphyrins are sensitive to O2 concentrations in the range of 0–160 Torr. The micelle-encapsulated QD-porphyrin assemblies have been employed for in vivo multiphoton imaging and lifetime-based oxygen measurements in mice with chronic dorsal skinfold chambers or cranial windows. Our results establish the utility of the QD-micelle approach for in vivo biological sensing applications.Chemistry and Chemical Biolog

Minimal information for studies of extracellular vesicles (MISEV2023): From basic to advanced approaches

Extracellular vesicles (EVs), through their complex cargo, can reflect the state of their cell of origin and change the functions and phenotypes of other cells. These features indicate strong biomarker and therapeutic potential and have generated broad interest, as evidenced by the steady year-on-year increase in the numbers of scientific publications about EVs. Important advances have been made in EV metrology and in understanding and applying EV biology. However, hurdles remain to realising the potential of EVs in domains ranging from basic biology to clinical applications due to challenges in EV nomenclature, separation from non-vesicular extracellular particles, characterisation and functional studies. To address the challenges and opportunities in this rapidly evolving field, the International Society for Extracellular Vesicles (ISEV) updates its 'Minimal Information for Studies of Extracellular Vesicles', which was first published in 2014 and then in 2018 as MISEV2014 and MISEV2018, respectively. The goal of the current document, MISEV2023, is to provide researchers with an updated snapshot of available approaches and their advantages and limitations for production, separation and characterisation of EVs from multiple sources, including cell culture, body fluids and solid tissues. In addition to presenting the latest state of the art in basic principles of EV research, this document also covers advanced techniques and approaches that are currently expanding the boundaries of the field. MISEV2023 also includes new sections on EV release and uptake and a brief discussion of in vivo approaches to study EVs. Compiling feedback from ISEV expert task forces and more than 1000 researchers, this document conveys the current state of EV research to facilitate robust scientific discoveries and move the field forward even more rapidly