Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations

In quantum chemistry calculations, the correlation energy is defined as the difference between the Hartree-Fock limit energy and the exact solution of the nonrelativistic Schrodinger equation. With this definition, the electron correlation effects are not directly observable. In this report, we show that the entanglement can be used as an alternative measure of the electron correlation in quantum chemistry calculations. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics. As an example we calculate the entanglement for He atom and H2 molecule with different basis sets.Comment: 12 pages, 2 figure

Perfect state distinguishability and computational speedups with postselected closed timelike curves

Bennett and Schumacher's postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch's model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement, and we discuss an important difference between "Deutschian" CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers.Comment: 15 pages, 4 figures; Foundations of Physics (2011

An Upper Palaeolithic Proto-writing System and Phenological Calendar

In at least 400 European caves such as Lascaux, Chauvet and Altamira, Upper Palaeolithic Homo sapiens groups drew, painted and engraved non-figurative signs from at least ~42,000 BP and figurative images (notably animals) from at least 37,000 BP. Since their discovery ~150 years ago, the purpose or meaning of European Upper Palaeolithic non-figurative signs has eluded researchers. Despite this, specialists assume that they were notational in some way. Using a database of images spanning the European Upper Palaeolithic, we suggest how three of the most frequently occurring signs—the line , the dot , and the —functioned as units of communication. We demonstrate that when found in close association with images of animals the line and dot constitute numbers denoting months, and form constituent parts of a local phenological/meteorological calendar beginning in spring and recording time from this point in lunar months. We also demonstrate that the sign, one of the most frequently occurring signs in Palaeolithic non-figurative art, has the meaning . The position of the within a sequence of marks denotes month of parturition, an ordinal representation of number in contrast to the cardinal representation used in tallies. Our data indicate that the purpose of this system of associating animals with calendar information was to record and convey seasonal behavioural information about specific prey taxa in the geographical regions of concern. We suggest a specific way in which the pairing of numbers with animal subjects constituted a complete unit of meaning—a notational system combined with its subject—that provides us with a specific insight into what one set of notational marks means. It gives us our first specific reading of European Upper Palaeolithic communication, the first known writing in the history of Homo sapiens

The Communication Cost of Simulating Bell Correlations

What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.Comment: 4 pages, 2 figures; reference adde

Optimal Management During Systemic Lupus Erythematosus Cesarean Section: An Educational Module

Abstract Importance: Systemic lupus erythematosus (SLE) is a lifelong multisystem autoimmune disorder characterized by the presence of autoantibodies that are directed against nuclear antigens. The disease is the most common type of lupus that has a heterogeneous presentation, and an affinity for the female gender with a peak onset in normative childbearing years. It becomes important for anesthesia providers to understand the potential complications that they may encounter during the obstetric management of this population, during cesarean sections. Recommendations that address the disease’s heterogeneous presentation and effect on the parturient organ systems provide a template for anesthesia providers during the perioperative management of the obstetric SLE patient. Objective: This quality improvement (QI) project aims to improve healthcare provider knowledge regarding the clinical implications of SLE, during the obstetric management for a cesarean section, to reduce morbidity and mortality for mother and newborn. Setting: A 716-bed acute care hospital in Broward County, Florida, which has a large obstetric population requiring anesthetic services. Anesthesia providers at this facility will be educated on the maternal-fetal dyad that can present during the management of the SLE mother during a cesarian section. Methods: A pretest survey will be administered to assess anesthesia providers’ knowledge, attitudes, and behaviors regarding the management of the SLE parturient during a cesarian section. An educational module will then be provided. Finally, a posttest survey containing the same questions as the pretest will be administered to participants. Results: Following the educational intervention, there was an increase in knowledge scores and stronger attitudes and beliefs regarding the role of anesthesia providers in the management of the SLE parturient during a cesarean section. Furthermore, most participants reported that they were highly likely to implement this into their clinical practice. Conclusion: An educational module can enhance anesthesia provider knowledge and increase the likelihood of improved outcomes for mother and neonate, during the anesthetic management of an SLE parturient during a cesarean section

Effects of Noisy Oracle on Search Algorithm Complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.Comment: 16 pages, 4 figures, submitted to Phys. Rev.

Region of fidelities for a 1 -> N universal qubit quantum cloner

We analyze a region of fidelities for qubit which is obtained after an application of a 1 -> N universal quantum cloner. We express the allowed region for fidelities in terms of overlaps of pure states with irreps of S(n) (n = N+1) showing that the pure states can be taken with real coefficients only. Subsequently, the case n = 4, corresponding to a 1 -> 3 cloner is studied in more detail as an illustrative example. To obtain the main result, we make a convex hull of possible ranges of fidelities related to a given irrep. The formalism allows to construct the state giving rise to a given N-tuple of fidelities.Comment: 13 pages, 3 figures, final version to appear in Physics Letters

Voltage-controlled coded qubit based on electron spin

We design and analyze a solid state qubit based on electron spin and controlled by electrical means. The coded qubit is composed of a three-electron complex in three tunable gated quantum dots. The two logical states of a qubit, |0L> and |1L>, reside in a degenerate subspace of total spin S=1/2 states. We demonstrate how applying voltages to specific gates changes the one-electron properties of the structure, and show how electron-electron interaction translates these changes into the manipulation of the two lowest energy states of the three-electron complex.Comment: 11 pages + 3 figure

An alternative approach to the construction of Schur-Weyl transform

We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to the system, results in a change of degrees of freedom, uncovering the information hidden in non-local degrees of freedom. This information can be used, inter alia, to study the structure of entangled states, their classification and may be useful for construction of quantum algorithms.Comment: 6 page