Mixed State Entanglement and Quantum Error Correction

Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbi- trary quantum state $|\xi\rangle$ can be transmitted at some rate Q through a noisy channel $\chi$ without degradation. We prove that an EPP involving one- way classical communication and acting on mixed state $\hat{M}(\chi)$ (obtained by sharing halves of EPR pairs through a channel $\chi$) yields a QECC on $\chi$ with rate $Q=D$, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one- and two-way classical communication respectively, and give an exact expression for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica- tion, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way com- munication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way com- munication is available. We exhibit a family of codes based on universal hash- ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single- error-correcting quantum block code. We prove that {\em iff} a QECC results in high fidelity for the case of no error the QECC can be recast into a form where the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82 pages latex including 19 postscript figures included using psfig macro

Adaptive protocols for the quantum depolarizing channel

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 81-85).In the first part, we present a family of entanglement purification protocols that generalize four previous methods, namely the recurrence method, the modified recurrence method, and the two methods proposed by Maneva-Smolin and Leung-Shor. We will show that this family of protocols have improved yields over a wide range of initial fidelities F, and hence imply new lower bounds on the quantum capacity assisted by two-way classical communication of the quantum depolarizing channel. In particular, we show that the yields of these protocols are higher than the yield of universal hashing for F less than 0.99999 and as F goes to 1. In the second part, we define, for any quantum discrete memoryless channel, quantum entanglement capacity with classical feedback, a quantity that lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication and the quantum capacity with classical feedback - are widely conjectured to be different. We then present adaptive protocols for this newly-defined quantity on the quantum depolarizing channel. These protocols in turn imply new lower bounds on the quantum capacity with classical feedback.by Alan W. Leung.Ph.D

Optical deep space communication via relay satellite

The possible use of an optical for high rate data transmission from a deep space vehicle to an Earth-orbiting relay satellite while RF links are envisioned for the relay to Earth link was studied. A preliminary link analysis is presented for initial sizing of optical components and power levels, in terms of achievable data rates and feasible range distances. Modulation formats are restricted to pulsed laser operation, involving bot coded and uncoded schemes. The advantage of an optical link over present RF deep space link capabilities is shown. The problems of acquisition, pointing and tracking with narrow optical beams are presented and discussed. Mathematical models of beam trackers are derived, aiding in the design of such systems for minimizing beam pointing errors. The expected orbital geometry between spacecraft and relay satellite, and its impact on beam pointing dynamics are discussed

X-ray spectra of the Fe-L complex II: atomic data constraints from EBIT experiment and X-ray grating observations of Capella

The Hitomi results for the Perseus cluster have shown that accurate atomic models are essential to the success of X-ray spectroscopic missions, and just as important as knowledge on instrumental calibration and astrophysical modeling. Preparing the models requires a multifaceted approach, including theoretical calculations, laboratory measurements, and calibration using real observations. In a previous paper, we presented a calculation of the electron impact cross sections on the transitions forming the Fe-L complex. In the present work, we systematically test the calculation against cross sections of ions measured in an electron beam ion trap experiment. A two-dimensional analysis in the electron beam energies and X-ray photon energies is utilized to disentangle radiative channels following dielectronic recombination, direct electron-impact excitation, and resonant excitation processes in the experimental data. The data calibrated through laboratory measurements are further fed into global modeling of the Chandra grating spectrum of Capella. We investigate and compare the fit quality, as well as sensitivity of the derived physical parameters to the underlying atomic data and the astrophysical plasma modeling. We further list the potential areas of disagreement between the observation and the present calculations, which in turn calls for renewed efforts in theoretical calculations and targeted laboratory measurements

Forward Error Correction for High Capacity Transmission Systems

Αυτή η μελέτη διερευνά την αλληλεπίδραση μεταξύ FEC διόρθωσης σφαλμάτων προώθησης και ψηφιακού αντιστάθμιση μη γραμμικότητας DBP σε ένα κανάλι ινών μεγάλων αποστάσεων. Πρώτον, α Η προσέγγιση που βασίζεται στην έρευνα χρησιμοποιείται για τον προσδιορισμό των τεχνολογιών αιχμής στο FEC για το κανάλι ινών και προσαρμόστε τα στο τελικό σχέδιο. Οι σχεδιαστικές επιλογές περιλαμβάνουν το χρήση τετριμμένων bit κωδικοποιημένης διαμόρφωσης αρχιτεκτονικής T-BICM με συνενωμένη σχήμα κώδικα που χρησιμοποιεί έναν επαναληπτικό soft αποκωδικοποιητή. Η απαίτηση για συνενωμένη Η εφαρμογή FEC οδήγησε σε μια άλλη έρευνα για έναν κώδικα καλής απόδοσης συνδυασμός. Το ακανόνιστο LDPC και το οιονεί κυκλικό QC-LDPC, που υιοθετήθηκαν από το DVB-S2 και Τα πρότυπα IEEE 802.11, αντίστοιχα, συνδυάστηκαν με τον κώδικα σκάλας και σύγκριση με βάση τις επιτευχθείσες επιδόσεις. Αποδεικνύουμε ότι αυξάνοντας τις ίνες απόσταση μετάδοσης κατά 1/3, από 300km έως 400km, διατηρώντας παράλληλα την η ίδια απόδοση και η χρήση των ίδιων γενικών εξόδων, δηλαδή 27,5% είναι εφικτό όταν υλοποίηση του DBP με 2 βήματα/περιοχή ή 3 βήματα/περιοχή, ανάλογα με το αν το Οι επαναλήψεις αποκωδικοποίησης είναι 10 ή 5. Αυτή η μελέτη καταλήγει με την εύνοια του LDPC από το DVB-S2 πάνω από το QC-LDPC του IEEE 802.11 για κανάλι ινών μεγάλων αποστάσεων. Το συμπέρασμα βγαίνει με βάση σχετικά με την καλύτερη απόδοση για το LDPC-DVB, λόγω των μεγάλων μηκών κωδικών του και του υποστήριξη για υψηλούς ρυθμούς κωδικοποίησης με αποτέλεσμα χαμηλές γενικές απαιτήσειςThis study investigates the interplay between forward error correction FEC and digital back-propagation DBP nonlinearity compensation on a long-haul fibre channel. First, a research-based approach is used to identify the state-of-the-art technologies in FEC for the fibre channel and adapt them to the final design. The design choices includes the usage of trivial bit interleaved coded modulation T-BICM architecture with a concatenated code scheme that uses an iterative soft decoder. The requirement for a concatenated FEC implementation motivated another investigation of a well-performing code combination. The Irregular LDPC and quasi-cyclic QC-LDPC, adopted from DVB-S2 and IEEE 802.11 standards, respectively, were each concatenated with staircase code and compared based on the attained performance. We prove that increasing the fibre transmission distance by a factor of 1/3, from 300km to 400km, while maintaining the same performance and using the same overhead, i.e. 27.5\% is achievable when implementing DBP with 2 steps/span or 3 steps/span, depending on whether the decoding iterations are 10 or 5. This study concludes with favouring LDPC from DVB-S2 over IEEE 802.11's QC-LDPC for long haul fibre channel. The conclusion is made based on the better attained performance for LDPC-DVB, due to its long code lengths, and its support for high coding rates resulting low overhead requirement

A NEW FRAMEWORK FOR MATERIAL INFORMATICS AND ITS APPLICATION TOWARD ELECTRIDE-HALIDE MATERIAL SYSTEMS

Despite many years of material exploration, the vast majority of unique crystalline materials remain undiscovered, and these undiscovered materials may offer stronger steels, better catalysts, improved transistors, and many other solutions to urgent societal problems. We therefore need a fast and efficient way of identifying new materials so that society can harness their benefits. To aid in accelerated materials discovery, this dissertation describes a computational framework designed for high-throughput calculations and analyses: the Simulated Materials Ecosystem (Simmate). This software allows users to explore various crystal databases, predict new materials, quickly calculate properties, and share results across analyses. We illustrate Simmate’s functionality through the exploration of an exotic class of materials known as electrides, which have gained considerable attention in recent literature thanks to their applications as superconductors, co-catalysts, and solid-state dopants. This diverse set of applications derives from an electride’s defining property: bare electrons that exist at isolated lattice sites. “Electride electrons” effectively serve as anions, which led us to propose the direct substitution of electrides with other -1 species, namely, halides (F-, Cl-, Br-, I-). Herein, we use Simmate to explore electride-halide systems, understand transitions between such materials, and predict new systems with enhanced material properties. This work ultimately led to the identification of novel ionic conductors, metastable electrides, and new search algorithms for discovering more of the same. Our framework and high-throughput search strategies are highly generalizable and will accelerate the exploration of many different materials beyond our illustrative examples with electride-halide material systems.Doctor of Philosoph

Nuclear Fusion Programme: Annual Report of the Association Karlsruhe Institute of Technology/EURATOM ; January 2011 - December 2011 (KIT Scientific Reports ; 7621)

The Karlsruhe Institute of Technology (KIT) is working in the framework of the European Fusion Programme on key technologies in the areas of superconducting magnets, microwave heating systems (Electron-Cyclotron-Resonance-Heating, ECRH), the deuterium-tritium fuel cycle, He-cooled breeding blankets, a He-cooled divertor and structural materials, as well as refractory metals for high heat flux applications including a major participation in the preparation of the international IFMIF project

Long distance free-space quantum key distribution

In the age of information and globalisation, secure communication as well as the protection of sensitive data against unauthorised access are of utmost importance. Quantum cryptography currently provides the only way to exchange a cryptographic key between two parties in an unconditionally secure fashion. Owing to losses and noise of today's optical fibre and detector technology, at present quantum cryptography is limited to distances below a few 100 km. In principle, larger distances could be subdivided into shorter segments, but the required quantum repeaters are still beyond current technology. An alternative approach for bridging larger distances is a satellite-based system, that would enable secret key exchange between two arbitrary points on the globe using free-space optical communication. The aim of the presented experiment was to investigate the feasibility of satellite-based global quantum key distribution. In this context, a free-space quantum key distribution experiment over a real distance of 144 km was performed. The transmitter and the receiver were situated in 2500 m altitude on the Canary Islands of La Palma and Tenerife, respectively. The small and compact transmitter unit generated attenuated laser pulses, that were sent to the receiver via a 15-cm optical telescope. The receiver unit for polarisation analysis and detection of the sent pulses was integrated into an existing mirror telescope designed for classical optical satellite communications. To ensure the required stability and efficiency of the optical link in the presence of atmospheric turbulence, the two telescopes were equipped with a bi-directional automatic tracking system. Still, due to stray light and high optical attenuation, secure key exchange would not be possible using attenuated pulses in connection with the standard BB84 protocol. The photon number statistics of attenuated pulses follows a Poissonian distribution. Hence, by removing a photon from all pulses containing two or more photons, an eavesdropper could measure its polarisation without disturbing the polarisation state of the remaining pulse. In this way, he can gain information about the key without introducing detectable errors. To protect against such attacks, the presented experiment employed the recently developed method of using additional "decoy" states, i.e., the the intensity of the pulses created by the transmitter were varied in a random manner. By analysing the detection probabilities of the different pulses individually, a photon-number-splitting attack can be detected. Thanks to the decoy-state analysis, the secrecy of the resulting quantum key could be ensured despite the Poissonian nature of the emitted pulses. For a channel attenuation as high as 35 dB, a secret key rate of up to 250 bit/s was achieved. Our outdoor experiment was carried out under real atmospheric conditions and with a channel attenuation comparable to an optical link from ground to a satellite in low earth orbit. Hence, it definitely shows the feasibility of satellite-based quantum key distribution using a technologically comparatively simple system