Quantum information theory of entanglement

Classical correlations are described consistently within classical information theory. This thesis presents a consistent quantum information theory of purely quantum correlations, i.e. entanglement. The main problem arises when we consider mixed states, for which it is difficult to separate quantum from purely classical correlations. This problem is the main subject of the thesis and is undertaken from two different perspectives. The first approach follows Shannon’s own approach, where we define a number of intuitively clear and physically sound conditions that a “good” measure of entanglement has to satisfy, and then search for measures satisfying these conditions. Our second approach is to extend the classical idea of distinguishing two probability distributions to quantum physics. The amount of entanglement will then determine the experimental ability to distinguish a given entangled state from a classical, disentangled state. We show that these two approaches have a number of features in common, leading to the same measures of entanglement. Classical information can be spoilt due to interactions with the environment. Classical information theory has a branch dealing with methods for protecting information called classical error correction. Quantum information is even more fragile and here we develop the quantum analogue of error correction. We develop a code that protects quantum states in the presence of spontaneous emission. We then show how to protect entanglement using this method. We also present a cavity QED implementation of various schemes aiming at increasing and protecting entanglement between two cavities using the standard Jaynes-Cummings interaction model between an atom and a cavity

Quantum Darwinism and Friends

In honor of Wojciech Zurek’s 70th birthday, this Special Issue is dedicated to recent advances in our understanding the emergence of classical reality, and pays tribute to Zurek’s seminal contributions to our understanding of the Universe. To this end, “Quantum Darwinism and Friends” collects articles that make sense of the apparent chasm between quantum weirdness and classical perception, and provides a snapshot of this fundamental, exciting, and vivid field of theoretical physics

Design and Synthesis of Efficient Circuits for Quantum Computers

Οι πρόσφατες εξελίξεις στον τομέα της πειραματικής κατασκευής κβαντικών υπολογιστών με εξαρτήματα αυξημένης αξιοπιστίας δείχνει ότι η κατασκευή τέτοιων μεγάλων μηχανών βασισμένων στις αρχές της κβαντικής φυσικής είναι πιθανή στο κοντινό μέλλον. Καθώς το μέγεθος των μελλοντικών κβαντικών υπολογιστών θα αυξάνεται, η σχεδίαση αποδοτικότερων κβαντικών κυκλωμάτων και μεθόδων σχεδίασης θα αποκτήσει σταδιακά πρακτικό ενδιαφέρον. Η συνεισφορά της διατριβής στην κατεύθυνση της σχεδίασης αποδοτικών κβαντικών κυκλωμάτων είναι διττή: Η πρώτη είναι η σχεδίαση καινοτόμων αποδοτικών αριθμητικών κβαντικών κυκλωμάτων βασισμένων στον Κβαντικό Μετασχηματισμό Fourier (QFT), όπως πολλαπλασιαστής-με-σταθερά-συσσωρευτής (MAC) και διαιρέτης με σταθερά, με γραμμικό βάθος (ή ταχύτητα) ως προς τον αριθμό ψηφίων των ακεραίων. Αυτά τα κυκλώματα συνδυάζονται αποτελεσματικά ώστε να επιτελέσουν την πράξη του modulo πολλαπλασιασμού με σταθερά με γραμμική πολυπλοκότητα χρόνου και χώρου και συνεπώς μπορούν να επιτελέσουν την πράξη της modulo εκθετικοποίησης (modular exponentiation) με τετραγωνική πολυπλοκότητα χρόνου και γραμμική πολυπλοκότητα χώρου. Οι πράξεις της modulo εκθετικοποίησης και του modulo πολλαπλασιασμού είναι αναπόσπαστα μέρη του σημαντικού κβαντικού αλγορίθμου παραγοντοποίησης του Shor, αλλά και άλλων κβαντικών αλγορίθμων της ίδιας οικογένειας, γνωστών ως κβαντική εκτίμηση φάσης (Quantum Phase Estimation). Αντιμετωπίζονται με αποτελεσματικό τρόπο σημαντικά προβλήματα υλοποίησης, που σχετίζονται με την απαίτηση χρήσης κβαντικών πυλών περιστροφής υψηλής ακρίβειας, καθώς και της χρήσης τοπικών επικοινωνιών. Η δεύτερη συνεισφορά της διατριβής είναι μία γενική μεθοδολογία ιεραρχικής σύνθεσης κβαντικών και αντιστρέψιμων κυκλωμάτων αυθαίρετης πολυπλοκότητας και μεγέθους. Η ιεραρχική μέθοδος σύνθεσης χειρίζεται καλύτερα μεγάλα κυκλώματα σε σχέση με τις επίπεδες μεθόδους σύνθεσης. Η προτεινόμενη μέθοδος προσφέρει πλεονεκτήματα σε σχέση με τις συνήθεις ιεραρχικές συνθέσεις που χρησιμοποιούν την μέθοδο "υπολογισμός-αντιγραφή-αντίστροφος υπολογισμός" του Bennett.The recent advances in the field of experimental construction of quantum computers with increased fidelity components shows that large-scale machines based on the principles of quantum physics are likely to be realized in the near future. As the size of the future quantum computers will be increased, efficient quantum circuits and design methods will gradually gain practical interest. The contribution of this thesis towards the design of efficient quantum circuits is two-fold. The first is the design of novel efficient quantum arithmetic circuits based on the Quantum Fourier Transform (QFT), like multiplier-with-constant-and-accumulator (MAC) and divider by constant, both of linear depth (or speed) with respect with the bits number of the integer operands. These circuits are effectively combined so as they can perform modular multiplication by constant in linear depth and space and consequently modular exponentiation in quadratic time and linear space. Modular exponentiation and modular multiplication operations are integral parts of the important quantum factorization algorithm of Shor and other quantum algorithms of the same family, known as Quantum Phase Estimation algorithms. Important implementation problems like the required high accuracy of the employed rotation quantum gates and the local communications between the gates are effectively addressed. The second contribution of this thesis is a generic hierarchical synthesis methodology for arbitrary complex and large quantum and reversible circuits. The methodology can handle more easily larger circuits relative to the flat synthesis methods. The proposed method offers advantages over the standard hierarchical synthesis which uses Bennett's method of "compute-copy-uncompute"

Quantum information theory

Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject \u27from the ground up\u27 it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quantum information theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo information, and the superactivation of quantum capacity. This book will be warmly welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists

From Classical to Quantum Shannon Theory

The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.Comment: v8: 774 pages, 301 exercises, 81 figures, several corrections; this draft, pre-publication copy is available under a Creative Commons Attribution-NonCommercial-ShareAlike license (see http://creativecommons.org/licenses/by-nc-sa/3.0/), "Quantum Information Theory, Second Edition" is available for purchase from Cambridge University Pres