125 research outputs found
Quantum Information with Continuous Variable systems
This thesis deals with the study of quantum communication protocols with
Continuous Variable (CV) systems. Continuous Variable systems are those
described by canonical conjugated coordinates x and p endowed with infinite
dimensional Hilbert spaces, thus involving a complex mathematical structure. A
special class of CV states, are the so-called Gaussian states. With them, it
has been possible to implement certain quantum tasks as quantum teleportation,
quantum cryptography and quantum computation with fantastic experimental
success. The importance of Gaussian states is two-fold; firstly, its structural
mathematical description makes them much more amenable than any other CV
system. Secondly, its production, manipulation and detection with current
optical technology can be done with a very high degree of accuracy and control.
Nevertheless, it is known that in spite of their exceptional role within the
space of all Continuous Variable states, in fact, Gaussian states are not
always the best candidates to perform quantum information tasks. Thus
non-Gaussian states emerge as potentially good candidates for communication and
computation purposes.Comment: PhD Thesis in Universitat Autonoma de Barcelona. Published by the
Lambert Academic Publishing (LAP) on March 18, 2011. ISBN-13:
978-3-8443-1948-
Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
We present a novel, detailed study on the usefulness of three-mode Gaussian
states states for realistic processing of continuous-variable quantum
information, with a particular emphasis on the possibilities opened up by their
genuine tripartite entanglement. We describe practical schemes to engineer
several classes of pure and mixed three-mode states that stand out for their
informational and/or entanglement properties. In particular, we introduce a
simple procedure -- based on passive optical elements -- to produce pure
three-mode Gaussian states with {\em arbitrary} entanglement structure (upon
availability of an initial two-mode squeezed state). We analyze in depth the
properties of distributed entanglement and the origin of its sharing structure,
showing that the promiscuity of entanglement sharing is a feature peculiar to
symmetric Gaussian states that survives even in the presence of significant
degrees of mixedness and decoherence. Next, we discuss the suitability of the
considered tripartite entangled states to the implementation of quantum
information and communication protocols with continuous variables. This will
lead to a feasible experimental proposal to test the promiscuous sharing of
continuous-variable tripartite entanglement, in terms of the optimal fidelity
of teleportation networks with Gaussian resources. We finally focus on the
application of three-mode states to symmetric and asymmetric telecloning, and
single out the structural properties of the optimal Gaussian resources for the
latter protocol in different settings. Our analysis aims to lay the basis for a
practical quantum communication with continuous variables beyond the bipartite
scenario.Comment: 33 pages, 10 figures (some low-res due to size constraints), IOP
style; (v2) improved and reorganized, accepted for publication in New Journal
of Physic
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
Practical unconditionally secure signature schemes and related protocols
The security guarantees provided by digital signatures are vital to many modern applications such as online banking, software distribution, emails and many more. Their ubiquity across digital communications arguably makes digital signatures one of the most important inventions in cryptography. Worryingly, all commonly used schemes – RSA, DSA and ECDSA – provide only computational security, and are rendered completely insecure by quantum computers. Motivated by this threat, this thesis focuses on unconditionally secure signature (USS) schemes – an information theoretically secure analogue of digital signatures. We present and analyse two new USS schemes. The first is a quantum USS scheme that is both information-theoretically secure and realisable with current technology. The scheme represents an improvement over all previous quantum USS schemes, which were always either realisable or had a full security proof, but not both. The second is an entirely classical USS scheme that uses minimal resources and is vastly more efficient than all previous schemes, to such an extent that it could potentially find real-world application. With the discovery of such an efficient classical USS scheme using only minimal resources, it is difficult to see what advantage quantum USS schemes may provide. Lastly, we remain in the information-theoretic security setting and consider two quantum protocols closely related to USS schemes – oblivious transfer and quantum money. For oblivious transfer, we prove new lower bounds on the minimum achievable cheating probabilities in any 1-out-of-2 protocol. For quantum money, we present a scheme that is more efficient and error tolerant than all previous schemes. Additionally, we show that it can be implemented using a coherent source and lossy detectors, thereby allowing for the first experimental demonstration of quantum coin creation and verification
Practical limitations on robustness and scalability of quantum Internet
As quantum theory allows for information processing and computing tasks that
otherwise are not possible with classical systems, there is a need and use of
quantum Internet beyond existing network systems. At the same time, the
realization of a desirably functional quantum Internet is hindered by
fundamental and practical challenges such as high loss during transmission of
quantum systems, decoherence due to interaction with the environment, fragility
of quantum states, etc. We study the implications of these constraints by
analyzing the limitations on the scaling and robustness of quantum Internet.
Considering quantum networks, we present practical bottlenecks for secure
communication, delegated computing, and resource distribution among end nodes.
Motivated by the power of abstraction in graph theory (in association with
quantum information theory), we consider graph-theoretic quantifiers to assess
network robustness and provide critical values of communication lines for
viable communication over quantum Internet.
In particular, we begin by discussing limitations on usefulness of isotropic
states as device-independent quantum key repeaters which otherwise could be
useful for device-independent quantum key distribution. We consider some
quantum networks of practical interest, ranging from satellite-based networks
connecting far-off spatial locations to currently available quantum processor
architectures within computers, and analyze their robustness to perform quantum
information processing tasks. Some of these tasks form primitives for delegated
quantum computing, e.g., entanglement distribution and quantum teleportation.
For some examples of quantum networks, we present algorithms to perform
different quantum network tasks of interest such as constructing the network
structure, finding the shortest path between a pair of end nodes, and
optimizing the flow of resources at a node.Comment: Happy about the successful soft landing of Chandrayaan-3 on the moon
by ISRO. 35 pages, 32 figures. Preliminary versio
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