Unitary transformations for testing Bell inequalities

It is shown that optical experimental tests of Bell inequality violations can be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of Sp(8,$\Bbb R$). In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post--selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.Comment: 3 figure

Lost and found: the radial quantum number of Laguerre-Gauss modes

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.Comment: Some minor typos fixed

BIOMECHANICAL STUDY ON CADAVER KNEE FOR THE EVALUATION OF CRUCIATE KNEE LIGAMENT RECONSTRUCTIONS

INTRODUCTION: Ruptures of the anterior and posterior cruciate knee ligament (ACL and PCL), alone or combined, are some of the most frequent joint injuries, especially in sports. The long-term unsatisfactory results and lack of systematic evaluation of surgical reconstructions have led us to undergo an evaluation on cadaver knees. MATERIAL AND METHOD: A preliminary study was performed on one cadaver knee. The femur was fixed on a holder and magnetic sensors “BirdsTM” were attached to the tibia and the femur, which tracked the knee’s movement. A threedimensional knee analyzer GENI(1) was used to calculate kinematic parameters (tibial internal and external rotation and ab/adduction), as well as ligament combined deformation (elongation / bending / torsion) during knee flexion. This experiment was performed on an intact knee and a knee where the PCL has been cut and reconstructed using a synthetic Trevia ligament. Finally the knee was dissected to produce a combined postero-lateral instability and reconstructed with and without postero-lateral corner reconstruction. The effect of different reconstruction methods on kinematics and ligament deformation were compared. RESULTS AND DISCUSSION: Kinematic parameters changed significantly when PCl and postero-lateral corner were dissected. The reconstruction of the PCL alone, using an “Over-the-Bottom” method described by Krudwig(2), shifted the curves back to the initial situation and decreased the variability of the movement. Ligament deformation was 3 mm elongation, 50o femoral flexion and 90o torsion. These values are in accordance with material properties and should lead to good long-term biofunctionnality. CONCLUSION: This study proposes an in vitro protocol for a better understanding of the clinical success or failure of different procedures. Preliminary results showed that the system and the protocol setup are sensitive to changes in kinematics following posterior cruciate ligament dissection and reconstruction. Experiments are performed at this time on several cadaver knees, in order to compare different reconstruction methods. REFERENCES: Sati, M. et al. (1997). Computer Assisted Knee Surgery: Diagnostics and Planning of Knee Surgery. Computer Aided Surgery 2, 108-123. Krudwig, W. (1997). In L'H. Yahia (Ed.), Ligaments and Ligamentoplasties. Heidelberg: Springer Verlag

Changes in physical education teachers’ beliefs regarding motivational strategies: A quasi-experimental study

Abstract Physical education teachers use motivational strategies that can (positively or negatively) affect their students’ level of motivation and engagement. Indeed, according to their experiences and beliefs, some teachers may focus on strategies that thwart, rather than support, students’ psychological needs (autonomy, competence, and relatedness). Effective professional development represents an excellent opportunity to help teachers use research-supported motivational strategies. Therefore, this study aimed to discover if attendance at a 2-day training course could positively affect PE teachers’ beliefs regarding empowering motivational strategies. Specifically, 11 PE teachers (experimental group = 6 [attending the training]; control group = 5 [no training]) from primary school (n = 6) and secondary school (n = 5) expressed their beliefs (effectiveness, feasibility, and normality) regarding 31 empowering motivational strategies proposed during training at the beginning (October) and the end (April) of the school year. Results of the Wilcoxon signed-rank test for related samples indicated no significant differences for the belief regarding effectiveness in either group. However, some positive significant changes (p ≤ .05) occurred in the experimental group for two motivational strategies supporting students’ need for autonomy and one supporting their need for competence. Given the small sample, positive trends (p ≤ .10) are also considered results of interest. In conclusion, the training appears likely to impact teachers’ beliefs. However, future professional development should provide additional feedback and follow-up time with teachers during experimentation with students to allow teachers to refine their understanding and use of the motivational strategies proposed

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

A complementarity-based approach to phase in finite-dimensional quantum systems

We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of this class consists of diagonal operators that represent amplitudes (or inversions). By the finite Fourier transform, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss the examples of qubits and qutrits, and show how these results generalize previous approaches.Comment: 6 pages, no figure

Quantum phases of a qutrit

We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.Comment: 6 page

Technical considerations in lateral extra-articular reconstruction coupled with anterior cruciate ligament reconstruction: a simulation study evaluating the influence of surgical parameters on control of knee stability

Background: Surgical parameters such as the selection of tibial and femoral attachment site, graft tension, and knee flexion angle at the time of fixation may influence the control of knee stability after lateral extra-articular reconstruction. This study aimed to determine how sensitive is the control of knee rotation and translation, during simulated pivot-shift scenarios, to these four surgery settings. Methods: A computer model was used to simulate 625 lateral extra-articular reconstructions based upon five different variations of each of the following parameters: femoral and tibial attachment sites, knee flexion angle and graft tension at the time of fixation. For each simulated surgery, the lateral extra-articular reconstruction external rotation moment at the knee joint center was computed during simulated pivot-shift scenarios. The sensitivity of the control of knee rotation and translation to a given surgery setting was assessed by calculating the coefficient of variation of the lateral extra-articular reconstruction external rotation moment. Findings: Graft tension had minimal influence on the control of knee rotation and translation with less than 2.4% of variation across the scenarios tested. Control of knee rotation and translation was the least affected by the femoral attachment site if the knee was close to full extension at the time of graft fixation. The choice of the tibial attachment site was crucial when the femoral fixation was proximal and posterior to the femoral epicondyle since 15 to 67% of variation was observed in the control of knee rotation and translation. Interpretation: Femoral and tibial attachment sites as well as knee flexion angle at the time of fixation should be considered by surgeons when performing lateral extra-articular reconstruction. Variation in graft tension between the ranges 20–40 N has minimal influence on the control of knee rotation and translation

Exchange Gate on the Qudit Space and Fock Space

We construct the exchange gate with small elementary gates on the space of qudits, which consist of three controlled shift gates and three "reverse" gates. This is a natural extension of the qubit case. We also consider a similar subject on the Fock space, but in this case we meet with some different situation. However we can construct the exchange gate by making use of generalized coherent operator based on the Lie algebra su(2) which is a well--known method in Quantum Optics. We moreover make a brief comment on "imperfect clone".Comment: Latex File, 12 pages. I could solve the problems in Sec. 3 in the preceding manuscript, so many corrections including the title were mad