A simple proof of the strong subadditivity inequality

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

Quantum entanglement in the two-impurity Kondo model

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, I. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, I, is at least several times larger than the Kondo temperature, T-K. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.

Entanglement and boundary critical phenomena

We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S-alpha, which includes the von Neumann entropy (alpha -> 1) and the single-copy entanglement (alpha ->infinity) as special cases. We identify the contribution of the boundaries to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g theorem, is a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.

Are echo techniques comparable for measurement of left ventricular dysynchrony? Comparison of real time 3D and tissue Doppler echocardiography in patients with ischaemic cardiomyopathy

Tissue Doppler (TD) assessment of dysynchrony (DYS) is established in evaluation for bi-ventricular pacing. Time to regional minimal volume by real-time 3D echo (3D) has been applied to DYS. 3D offers simultaneous assessment of all segments and may limit errors in localization of maximum delay due to off-axis images.We compared TD and 3D for assessment of DYS. 27 patients with ischaemic cardiomyopathy (aged 60±11 years, 85% male) underwent TD with generation of regional velocity curves. The interval between QRS onset and maximal systolic velocity (TTV) was measured in 6 basal and 6 mid-cavity segments. Onthe same day,3Dwas performed and data analysed offline with Q-Lab software (Philips, Andover, MA). Using 12 analogous regional time-volume curves time to minimal volume (T3D)was calculated. The standard deviation (S.D.) between segments in TTV and T3D was calculated as a measure ofDYS. In 7 patients itwas not possible to measureT3D due to poor images. In the remaining 20, LV diastolic volume, systolic volume and EF were 128±35 ml, 68±23 ml and 46±13%, respectively. Mean TTV was less than mean T3D (150±33ms versus 348±54 ms; p < 0.01). The intrapatient range was 20–210ms for TTV and 0–410ms for T3D. Of 9 patients (45%) with significantDYS (S.D. TTV > 32 ms), S.D. T3D was 69±37ms compared to 48±34ms in those without DYS (p = ns). In DYS patients there was concordance of the most delayed segment in 4 (44%) cases.Therefore, different techniques for assessing DYS are not directly comparable. Specific cut-offs for DYS are needed for each technique.

High-fidelity Z-measurement error encoding of optical qubits

We demonstrate a quantum error correction scheme that protects against accidental measurement, using a parity encoding where the logical state of a single qubit is encoded into two physical qubits using a nondeterministic photonic controlled-NOT gate. For the single qubit input states vertical bar 0 >, vertical bar 1 >, vertical bar 0 > +/- vertical bar 1 >, and vertical bar 0 > +/- i vertical bar 1 > our encoder produces the appropriate two-qubit encoded state with an average fidelity of 0.88 +/- 0.03 and the single qubit decoded states have an average fidelity of 0.93 +/- 0.05 with the original state. We are able to decode the two-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 one-qubit decoded states arising from 16 real and imaginary single-qubit superposition inputs have an average fidelity of 0.96 +/- 0.03.

Constructing internationally comparable real income aggregates by combining sparse benchmark data with annual national accounts data: A state-space approach

The importance of availability of comparable real income aggregates and their components to applied economic research is highlighted by the popularity of the Penn World Tables. Any methodology designed to achieve such a task requires the combination of data from several sources. The first is purchasing power parities (PPP) data available from the International Comparisons Project roughly every five years since the 1970s. The second is national level data on a range of variables that explain the behaviour of the ratio of PPP to market exchange rates. The final source of data is the national accounts publications of different countries which include estimates of gross domestic product and various price deflators. In this paper we present a method to construct a consistent panel of comparable real incomes by specifying the problem in state-space form. We present our completed work as well as briefly indicate our work in progress.

Ultrasonic measurement technique of burning metals in normal and reduced gravity

The in situ real time measurement of the regression rate of a melting interface (RRMI) is performed by the ultrasonic measurement system reported here. The RRMI is the rate at which a solid/liquid interface (SLI) moves along a metallic rod while burning in an oxygen-enriched atmosphere and is an important flatnmability indicator. The ultrasonic transducer and associated equipment used to drive the transducer and record the echo signal is described, along with the process that transforms the acquired signals into a RRMI value. Test rods of various metals and geometric shapes were burned at several test conditions in different test facilities. The RRMI results with quantified errors are presented and reviewed. The effect of reduced gravity on burning metals is important to space-applications and RRMI results obtained in a reduced gravity environment are also presented.