Quantum nonlocality in two three-level systems

Recently a new Bell inequality has been introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)], which is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a nonmaximally entangled state. It is shown that the resistance to noise is not a good measure of nonlocality and we introduce some other possible measures. The nonmaximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two von Neumann measurements per party may be not optimal for detecting nonlocality. For d=3,4, we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal von Neumann settings, is distillable.

Quantum nonlocality, cryptography and complexity

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Genesis of quantum nonlocality

We revisit the problem of an otherwise classical particle immersed in the zero-point radiation field, with the purpose of tracing the origin of the nonlocality characteristic of Schrodinger`s equation. The Fokker-Planck-type equation in the particles phase-space leads to an infinite hierarchy of equations in configuration space. In the radiationless limit the first two equations decouple from the rest. The first is the continuity equation: the second one, for the particle flux, contains a nonlocal term due to the momentum fluctuations impressed by the field. These equations are shown to lead to Schrodinger`s equation. Nonlocality (obtained here for the one-particle system) appears thus as a property of the description, not of Nature. (C) 2011 Elsevier B.V. All rights reserved.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.

Better Bell-inequality violation by collective measurements

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

On the nonlocality of the quantum channel in the standard teleportation protocol

By exhibiting a violation of a novel form of the Bell-CHSH inequality, Żukowski has recently established that the quantum correlations exploited in the standard perfect teleportation protocol cannot be recovered by any local hidden variables model. In the case of imperfect teleportation, we show that a violation of a generalized form of Żukowski's teleportation inequality can only occur if the channel state, considered by itself, already violates a Bell-CHSH inequality. On the other hand, the fact that the channel state violates a Bell-CHSH inequality is not sufficient to imply a violation of Żukowski's teleportation inequality (or any of its generalizations). The implication does hold, however, if the fidelity of the teleportation exceeds ≈ 0.90. © 2001 Elsevier Science B.V. All rights reserved.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Comment on "Canonical formalism for Lagrangians with nonlocality of finite extent"

The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this Comment we propose that this conclusion is false.

Pauli nonlocality in heavy-ion rainbow scattering: A further test of the folding model

Nonlocal interactions are an intrinsically quantum phenomenon. In this work we point out that, in the context of heavy ions, such interactions can be studied through the refractive elastic scattering of these systems at intermediate energies. We show that most of the observed energy dependence of the local equivalent bare potential arises from the exchange nonlocality. The nonlocality parameter extracted from the data was found to be very close to the one obtained from folding models. The effective mass of the colliding, heavy-ion, system was found to be close to the nucleon effective mass in nuclear matter.

Quantum Dots As Biophotonics Tools.

This chapter provides a short review of quantum dots (QDs) physics, applications, and perspectives. The main advantage of QDs over bulk semiconductors is the fact that the size became a control parameter to tailor the optical properties of new materials. Size changes the confinement energy which alters the optical properties of the material, such as absorption, refractive index, and emission bands. Therefore, by using QDs one can make several kinds of optical devices. One of these devices transforms electrons into photons to apply them as active optical components in illumination and displays. Other devices enable the transformation of photons into electrons to produce QDs solar cells or photodetectors. At the biomedical interface, the application of QDs, which is the most important aspect in this book, is based on fluorescence, which essentially transforms photons into photons of different wavelengths. This chapter introduces important parameters for QDs' biophotonic applications such as photostability, excitation and emission profiles, and quantum efficiency. We also present the perspectives for the use of QDs in fluorescence lifetime imaging (FLIM) and Förster resonance energy transfer (FRET), so useful in modern microscopy, and how to take advantage of the usually unwanted blinking effect to perform super-resolution microscopy.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Interplay Of Weak Interactions In The Atom-by-atom Condensation Of Xenon Within Quantum Boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined 'quantum boxes'. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on-but is not limited to-the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

Measurement Of The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy Excluding Blinking.

One of the most important properties of quantum dots (QDs) is their size. Their size will determine optical properties and in a colloidal medium their range of interaction. The most common techniques used to measure QD size are transmission electron microscopy (TEM) and X-ray diffraction. However, these techniques demand the sample to be dried and under a vacuum. This way any hydrodynamic information is excluded and the preparation process may alter even the size of the QDs. Fluorescence correlation spectroscopy (FCS) is an optical technique with single molecule sensitivity capable of extracting the hydrodynamic radius (HR) of the QDs. The main drawback of FCS is the blinking phenomenon that alters the correlation function implicating in a QD apparent size smaller than it really is. In this work, we developed a method to exclude blinking of the FCS and measured the HR of colloidal QDs. We compared our results with TEM images, and the HR obtained by FCS is higher than the radius measured by TEM. We attribute this difference to the cap layer of the QD that cannot be seen in the TEM images.