9 research outputs found
Low dimensional bound entanglement with one-way distillable cryptographic key
We provide a class of bound entangled states that have positive distillable
secure key rate. The smallest state of this kind is , which shows
that peculiar security contained in bound entangled states does not need high
dimensional systems. We show, that for these states a positive key rate can be
obtained by {\it one-way} Devetak-Winter protocol. Subsequently the volume of
bound entangled key-distillable states in arbitrary dimension is shown to be
nonzero. We provide a scheme of verification of cryptographic quality of
experimentally prepared state in terms of local observables. Proposed set of 7
collective settings is proven to be optimal in number of settings.Comment: 5 pages, ReVTex
Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
As with classical information, error-correcting codes enable reliable
transmission of quantum information through noisy or lossy channels. In
contrast to the classical theory, imperfect quantum channels exhibit a strong
kind of synergy: there exist pairs of discrete memoryless quantum channels,
each of zero quantum capacity, which acquire positive quantum capacity when
used together. Here we show that this "superactivation" phenomenon also occurs
in the more realistic setting of optical channels with attenuation and Gaussian
noise. This paves the way for its experimental realization and application in
real-world communications systems.Comment: 5 pages, 4 figures, one appendi
Limitations on Quantum Key Repeaters
A major application of quantum communication is the distribution of entangled
particles for use in quantum key distribution (QKD). Due to noise in the
communication line, QKD is in practice limited to a distance of a few hundred
kilometres, and can only be extended to longer distances by use of a quantum
repeater, a device which performs entanglement distillation and quantum
teleportation. The existence of noisy entangled states that are undistillable
but nevertheless useful for QKD raises the question of the feasibility of a
quantum key repeater, which would work beyond the limits of entanglement
distillation, hence possibly tolerating higher noise levels than existing
protocols. Here we exhibit fundamental limits on such a device in the form of
bounds on the rate at which it may extract secure key. As a consequence, we
give examples of states suitable for QKD but unsuitable for the most general
quantum key repeater protocol.Comment: 11+38 pages, 4 figures, Statements for exact p-bits weakened as
non-locking bound on measured relative entropy distance contained an erro
Public Quantum Communication and Superactivation
Is there a meaningful quantum counterpart to public communication? We argue
that the symmetric-side channel -- which distributes quantum information
symmetrically between the receiver and the environment -- is a good candidate
for a notion of public quantum communication in entanglement distillation and
quantum error correction.
This connection is partially motivated by [Brand\~ao and Oppenheim,
arXiv:1004.3328], where it was found that if a sender would like to communicate
a secret message to a receiver through an insecure quantum channel using a
shared quantum state as a key, then the insecure quantum channel is only ever
used to simulate a symmetric-side channel, and can always be replaced by it
without altering the optimal rate. Here we further show, in complete analogy to
the role of public classical communication, that assistance by a symmetric-side
channel makes equal the distillable entanglement, the recently-introduced
mutual independence, and a generalization of the latter, which quantifies the
extent to which one of the parties can perform quantum privacy amplification.
Symmetric-side channels, and the closely related erasure channel, have been
recently harnessed to provide examples of superactivation of the quantum
channel capacity. Our findings give new insight into this non-additivity of the
channel capacity and its relation to quantum privacy. In particular, we show
that single-copy superactivation protocols with the erasure channel, which
encompasses all examples of non-additivity of the quantum capacity found to
date, can be understood as a conversion of mutual independence into distillable
entanglement.Comment: 10 page
Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity
We prove unconditional security for a quantum key distribution (QKD) protocol
based on distilling pbits (twisted ebits) [quant-ph/0309110] from an arbitrary
untrusted state that is claimed to contain distillable key. Our main result is
that we can verify security using only public communication -- via parameter
estimation of the given untrusted state. The technique applies even to bound
entangled states, thus extending QKD to the regime where the available quantum
channel has zero quantum capacity. We also show how to convert our
purification-based QKD schemes to prepare-measure schemes.Comment: Final version for IEEE TI
Entanglement and non local correlations: quantum resources for information processing
Quantum Information Theory (QIT) studies how information can be processed and transmitted when encoded on quantum states. Practically, it can be understood as the effort to generalize Classical Information Theory to the quantum world. Interestingly, the fact that very-small scale Physics differs considerably from that of macroscopic objects offers a richer structure to the new theory. Among other phenomena, entanglement is at the heart of many quantum information protocols. It is the most spectacular and counter-intuitive manifestation of quantum mechanics: it signifies the existence of non-local correlations. Although intrinsically non-intuitive, these strange effects have been shown to lead to intriguing applications with no classical analogue. The main scope of this thesis is to establish qualitative and quantitative connections among the different quantum and classical information resources. Among the many weird effects that quantum systems present, the non-additivity concept plays an important role. In the quantum realm, the joint processing of two quantum resources is often better than the sum of the two resources. Activation is the strongest manifestation of non-additivity. It can be understood as the capability of two objects to achieve a given task that is impossible for each of them when considered individually. From a classical point of view, it is unknown whether such a process can hold. Here we focus on the classical secret-key rate. We provide two probability distributions conjectured to have bound information, hence from which it is conjectured that no secret key can be extracted when taken individually, but that lead to a positive secret-key rate when combined. For that, we exploit the close connection between the information-theoretic key agreement and the quantum entanglement scenario. Successively, we move to the multipartite scenario showing a one-to-one correspondence between bound information and bound entanglement. We provide an example of multipartite bound information which shares the same features of its quantum analogue, the Smolin state. Later, we move to prove a deep connection between privacy and non-locality. We do it by showing that all private states violate the Bell-CHSH inequality. Private states are those entangled states from which a perfectly secure cryptographic key can be extracted. An example of those is the maximally entangled state. But still, there are other private states that are not maximally entangled. While a maximally entangled state violates a Bell's inequality, this is not known a priori for the whole set. We give a general proof valid for any dimension and any number of parties. Private states, then, not only represent the unit of quantum privacy, but also allow two distant parties to establish a different quantum resource, namely non-local correlations. Lastly, we tackle the connection between non-locality and genuine randomness. Non-locality and genuine intrinsic randomness have been the subject of active interest since the early days of quantum physics. Initially, this interest was mainly derived from their foundational and fundamental implications but recently it also has acquired a practical aspect. Recent development in device independent scenario have heightened the need to quantify both the randomness and non-locality inherent in quantum systems. While some works try to deepen this relation, we provide a simple method to detect Bell tests that allow the certification of maximal randomness. These arguments exploit the symmetries of Bell inequalities and assume the uniqueness of the quantum probability distribution maximally violating it. We show how these arguments can be applied to intuit the randomness intrinsic in a probability distribution without resorting to numerical calculations.La Teoría de la Información Cuántica (QIT) estudia como la información puede ser procesada y transmitida al codificarse en estados cuánticos. Prácticamente, se puede pensar como la generalización de la Teoría de Información Clásica al mundo cuántico.
El hecho que la física a esta escala difiera considerablemente de aquella de los objetos macroscópicos ofrece una mayor riqueza a la estructura de la nueva teoría. Entre otros fenómenos, el entrelazamiento está a la base de muchos protocolos cuánticos. Es la más espectacular y anti-intuitiva manifestación de la mecánica cuántica observada en sistemas cuánticos compuestos: implica la existencia de correlaciones no-locales. No obstante la extrañeza de estos efectos, se han demostrado distintas aplicaciones sin ningún análogo clásico. El objetivo de esta tesis es establecer conexiones cualitativas y cuantitativas entre los diferentes recursos descritos por la teoría cuántica y clásica. Entre los efectos raros que los sistemas cuánticos muestran, la no-aditividad desempeña un papel muy importante. En el mundo cuántico, el uso de dos recursos cuánticos puede ser más ventajoso que la suma de los dos, considerados individualmente. La activación es
la mas fuerte manifestación del fenómeno de no-aditividad. Este proceso se puede entender como la capacidad de dos objetos juntos de lograr una tarea que sería imposible por cada uno de ellos singularmente. Desde un punto de vista clásico, es desconocido si existen procesos o cantidades que no respetan la aditividad. Aquí, nos centramos en la tasa de clave secreta. Presentamos aquí dos distribuciones de probabilidad que conjeturamos contener bound information, o sea a partir de la cuales es imposible destilar bits secretos que dan bits secretos cuando utilizadas conjuntamente. Para probar este resultado, utilizamos la conexión existente entre entrelazamiento y el proceso de establecimiento de seguridad.
Sucesivamente desplazándonos al caso multipartito, probamos una correspondencia uno a uno entre la bound information y el entrelazamiento no-destilable. Presentamos un ejemplo de bound information multipartita que comparte las mismas propiedades de su análogo cuántico, el estado de Smolin. Luego profundizamos la relación entre privacidad y no-localidad. Probamos que todos los estados que pertenecen al conjunto de estados privados violan una desigualdad de Bell, conocida como CHSH. Los estados privados son aquellos estados entrelazados de los cuales es posible extraer una clave secreta.
Un ejemplo de estos estados es el estado máximamente entrelazado, pero hay otros que son privados aunque no máximamente entrelazados. Es conocido que un estado máximamente entrelazado puede violar una desigualdad de Bell, pero lo que se desconoce es si esto pasa para todos los estados privados. Nuestro resultado es general ya que nuestra prueba es válida para cualquier número de partes y cualquier dimensión del espacio local de cada una. Los estados privados, entonces, no solo permiten destilar una clave de forma segura sino que también presentan una propiedad tan fuerte como la no-localidad. Finalmente, investigamos la relación entre los conceptos de no-localidad y de aleatoriedad.
Desde los orígenes de la teoría cuántica, los conceptos de no-localidad y de aleatoriedad fueron objeto de gran interés. A principio este interés se debía más a razones relacionadas con los fundamentos de la teoría, pero recientes resultados han empujado la comunidad científica a investigar ulteriormente y sobre todo a cuantificar la no-localidad y la aleatoriedad presente en los estados cuánticos. Aunque algunos autores se hayan movido en esta direccion, muchas preguntas han quedado sin respuestas. Aquí presentamos un simple método que permite detectar aquellas desigualdades de Bell que pueden certificar la presencia de máxima aleatoriedad. Nuestros resultados prueban como simples argumentos pueden dar complejas respuestas sin la necesidad de recorrer a computaciones numéricas
Informationsübertragung durch Quantenkanäle
This PhD thesis represents work done between Aug. 2003 and Dec. 2006 in Reinhard F. Werner's quantum information theory group at Technische Universität Braunschweig, and Artur Ekert's Centre for Quantum Computation at the University of Cambridge. Quantum information science combines ideas from physics, computer science and information theory to investigate how quintessentially quantum mechanical effects such as superposition and entanglement can be employed for the handling and transfer of information. My thesis falls into the field of abstract quantum information theory, which is concerned with the fundamental resources for quantum information processing and their interconversion and tradeoffs. Every such processing of quantum information can be represented as a quantum channel: a completely positive and trace-preserving map between observable algebras associated to physical systems. This work investigates both fundamental properties of quantum channels (mostly in Chs. 3 and 4) and their asymptotic capacities for classical as well as quantum information transfer (in Chs. 5 through 8).Diese Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) entstand zwischen August 2003 und Dezember 2006 in Prof. Reinhard F. Werners Arbeitsgruppe Quanteninformationstheorie an der Technischen Universität Braunschweig und Prof. Artur Ekerts Centre for Quantum Computation an der Universität Cambridge. Die Quanteninformationswissenschaft untersucht mit den Ideen und Methoden der Physik, der Informatik und der Informationstheorie, wie sich charakteristisch quantenphysikalische Effekte, beispielsweise Superposition und Verschränkung, zur Verarbeitung und Übertragung von Information nutzbar machen lassen. Die vorliegende Dissertation fällt in das Gebiet der abstrakten Quanteninformationstheorie, die die grundlegenden Ressourcen für die Verarbeitung von Quanteninformation sowie deren Wechselbeziehungen und Abhängigkeiten untersucht. Eine jede solche Verarbeitung von Quanteninformation läßt sich mathematisch beschreiben als sogenannter Quantenkanal, eine vollständig positive und spurerhaltende Abbildung zwischen den physikalischen Systemen zugeordneten Observablen-Algebren. In dieser Arbeit werden sowohl grundlegende Eigenschaften solcher Quantenkanäle (vor allem in den Kap. 3 und Kap. 4) als auch ihre asymptotischen Kapazitäten für die Übertragung von klassischer Information und Quanteninformation (in Kap. 5 bis 8) untersucht