Limitations of Passive Protection of Quantum Information

The ability to protect quantum information from the effect of noise is one of the major goals of quantum information processing. In this article, we study limitations on the asymptotic stability of quantum information stored in passive N-qubit systems. We consider the effect of small imperfections in the implementation of the protecting Hamiltonian in the form of perturbations or weak coupling to a ground state environment. We prove that, regardless of the protecting Hamiltonian, there exists a perturbed evolution that necessitates a final error correcting step when the state of the memory is read. Such an error correction step is shown to require a finite error threshold, the lack thereof being exemplified by the 3D compass model. We go on to present explicit weak Hamiltonian perturbations which destroy the logical information stored in the 2D toric code in a time O(log(N)).Comment: 17 pages and appendice

Quantum memory

This thesis is devoted to the study of coherent storage of quantum information as well as its potential applications. Quantum memories are crucial to harnessing the potential of quantum physics for information processing tasks. They are required for almost all quantum computation proposals. However, despite the large arsenal of theoretical techniques and proposals dedicated to their implementation, the realization of long-lived quantum memories remains an elusive task. Encoding information in quantum states associated to many-body topological phases of matter and protecting them by means of a static Hamiltonian is one of the leading proposals to achieve quantum memories. While many genuine and well publicized virtues have been demonstrated for this approach, equally real limitations were widely disregarded. In the first two projects of this thesis, we study limitations of passive Hamiltonian protection of quantum information under two different noise models. Chapter 2 deals with arbitrary passive Hamiltonian protection for a many body system under the effect of local depolarizing noise. It is shown that for both constant and time dependent Hamiltonians, the optimal enhancement over the natural single-particle memory time is logarithmic in the number of particles composing the system. The main argument involves a monotonic increase of entropy against which a Hamiltonian can provide little protection. Chapter 3 considers the recoverability of quantum information when it is encoded in a many-body state and evolved under a Hamiltonian composed of known geometrically local interactions and a weak yet unknown Hamiltonian perturbation. We obtain some generic criteria which must be fulfilled by the encoding of information. For specific proposals of protecting Hamiltonian and encodings such as Kitaev's toric code and a subsystem code proposed by Bacon, we additionally provide example perturbations capable of destroying the memory which imply upper bounds for the provable memory times. Chapter 4 proposes engineered dissipation as a natural solution for continuously extracting the entropy introduced by noise and keeping the accumulation of errors under control. Persuasive evidence is provided supporting that engineered dissipation is capable of preserving quantum degrees of freedom from all previously considered noise models. Furthermore, it is argued that it provides additional flexibility over Hamiltonian thermalization models and constitutes a promising approach to quantum memories. Chapter 5 introduces a particular experimental realization of coherent storage, shifting the focus in many regards with respect to previous chapters. First of all, the system is very concrete, a room-temperature nitrogen-vacancy centre in diamond, which is subject to actual experimental control and noise restrictions which must be adequately modelled. Second, the relevant degrees of freedom reduce to a single electronic spin and a carbon 13 spin used to store a qubit. Finally, the approach taken to battle decoherence consists of inducing motional narrowing and applying dynamical decoupling pulse sequences, and is tailored to address the systems dominant noise sources. Chapter 6 analyses unforgeable tokens as a potential application of these room-temperature qubit memories. Quantum information protocols based on Wiesner's quantum money scheme are proposed and analysed. We provide the first rigorous proof that such unentangled tokens may be resistant to counterfeiting attempts while tolerating a certain amount of noise. In summary, this thesis provides contributions to quantum memories in four different aspects. Two projects were dedicated to understanding and exposing the limitations of existing proposals. This is followed by a constructive proposal of a new counter-intuitive theoretical model for quantum memories. An applied experimental project achieves record coherent storage times in room-temperature solids. Finally, we provide rigorous analysis for a quantum information application of quantum memories. This completes a broad picture of quantum memories which integrates different perspectives, from theoretical critique and constructive proposal, to technological application going through a down-to-earth experimental implementation

Using quantum key distribution for cryptographic purposes: a survey

The appealing feature of quantum key distribution (QKD), from a cryptographic viewpoint, is the ability to prove the information-theoretic security (ITS) of the established keys. As a key establishment primitive, QKD however does not provide a standalone security service in its own: the secret keys established by QKD are in general then used by a subsequent cryptographic applications for which the requirements, the context of use and the security properties can vary. It is therefore important, in the perspective of integrating QKD in security infrastructures, to analyze how QKD can be combined with other cryptographic primitives. The purpose of this survey article, which is mostly centered on European research results, is to contribute to such an analysis. We first review and compare the properties of the existing key establishment techniques, QKD being one of them. We then study more specifically two generic scenarios related to the practical use of QKD in cryptographic infrastructures: 1) using QKD as a key renewal technique for a symmetric cipher over a point-to-point link; 2) using QKD in a network containing many users with the objective of offering any-to-any key establishment service. We discuss the constraints as well as the potential interest of using QKD in these contexts. We finally give an overview of challenges relative to the development of QKD technology that also constitute potential avenues for cryptographic research.Comment: Revised version of the SECOQC White Paper. Published in the special issue on QKD of TCS, Theoretical Computer Science (2014), pp. 62-8

How long can a quantum memory withstand depolarizing noise?

We investigate the possibilities and limitations of passive Hamiltonian protection of a quantum memory against depolarizing noise. Without protection, the lifetime of a single qubit is independent of N, the number of qubits composing the memory. In the presence of a protecting Hamiltonian, the lifetime increases at most logarithmically with N. We construct an explicit time-independent Hamiltonian which saturates this bound, exploiting the noise itself to achieve the protection.Comment: 4 pages, 2 figures. Accepted version, Journal-Ref adde