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Unless stated otherwise, the seminars are on Wednesdays, 11:30am-12:20pm, in the Bright building, room 516. If you have questions, please contact Andreas Klappenecker.
Spring 2006
Network coding is a new research area. It was originally proposed to improve the network throughput. In network coding, the router will combine the packets from different sources by coding and then send encoded packets out instead of simple forwarding. In this talk, I will present some basic theory of network coding and its applications. For the theory part, I will talk about Max-Flow Min-Cut theorem and some results on deterministic and randomized network coding. For the applications of network coding, I will introduce its usage and benefits in content distribution, wireless networking, and security area.
We consider Raman scattered photons from a molecule driven by N lasers for microscopically resolving the distance between two molecules. We show that N-photon correlation allows us to beat the Rayleigh diffraction limit by a factor of 2^N. From the stand point of quantum information, the N photons arise from separate two-level transitions in the molecule, and this contributes to an exponential scaling in interference pathways in the multi-photon correlation. We achieve the conversion of the time-frequency entanglement of the photons to the spatial domain with a separated detector arrangement. A lock in technique matches the Rabi and optical frequencies to gain more precise information about the source separation.
Leader election is an important task in distributed systems. However, there are no deterministic algorithms for electing a leader when the underlying topology is anonymous, i.e., the processors do not have unique identifiers. There exist some randomized leader election algorithms but they are not guaranteed to terminate. In this talk, we will present two quantum algorithms for leader election that were recently independently proposed by Tani et al. and D'Hondt et al. These algorithms always terminate and elect a leader in anonymous networks. They demonstrate that apart from providing a speedup of running time, quantum computing can have another significant advantage over classical computing in that problems unsolvable in the classical distributed setting maybe solvable in the quantum scenario.
Shpilrain and Ushakov proposed a key exchange protocol as an alternative to the well-known cryptographic key establishment protocols such as RSA or Diffie-Hellman. The hardness of the proposed protocol depends on a group-theoretic decomposition problem. In this talk, we give an exposition of this protocol, present background material, and discuss some crypto-analytic aspects.
It is shown that the original Kirchhoff-loop-Johnson(-like)-noise (KLJN) cipher is naturally protected against the man-in-the-middle (MITM) attack, if the eavesdropper is using resistors and noise voltage generators just like the sender and the receiver. The eavesdropper can extract zero bit of information before she is discovered. However, when the eavesdropper is using noise current generators, though the cipher is protected, the eavesdropper may still be able to extract one bit of information while she is discovered. For enhanced security, we expand the KLJN cipher with the comparison of the instantaneous voltages via the public channel. In this way, the sender and receiver have a full control over the security of measurable physical quantities in the Kirchhoff-loop. We show that when the sender and receiver compare not only their instantaneous current data but also their instantaneous voltage data then the zero-bit security holds even for the noise current generator case. We show that the original KLJN scheme is also zero-bit protected against that type of MITM attack when the eavesdropper uses voltage noise generators, only. In conclusion, within the idealized model scheme, the man-in-the-middle-attack does not provide any advantage compared to the regular attack considered earlier. The remaining possibility is the attack by a short, large current pulse, which described in the original paper as the only efficient type of regular attacks, and that yields the one bit security. In conclusion, the KLJN cipher is superior to known quantum communication schemes in every respect, including speed, robustness, maintenance need, price and its natural immunity against the man-in-the-middle attack.
Fall 2005
Part 2.
The conference is here at Texas A&M. Registration is free.
We review the ABL formula and point out that any state reduction which induces a quantum teleportation has no retrodictive impact.
We propose an energy efficient protocol for sensor data management. The protocol employs replicated data sinks to achieve (1) resiliency to data sink failure, and (2) efficiency in storing and retrieving sensor data. A simple address assignment scheme is introduced that partitions the sensor field into cells, where each cell contains one data sink and all sensors that are closest to this data sink. We show that this scheme is scalable and resilient against data sink and sensor node failures. Furthermore, the scheme has a reasonably low message complexity and high energy efficiency.This is joint work with Hyunyoung Lee, Kyoungsook Lee, and Lan Lin.
An absolutely secure, fast, inexpensive, robust, dust and vibration resistant, maintenance-free and low-power-consumption communication is proposed. The states of the information bit are represented by two resistance values. The sender and the receiver have such resistors available and they randomly select and connect one of them to the channel at the beginning of each clock period. The thermal noise voltage and current can be observed but Kirchoff's law provides only a second-order equation. A secure bit is communicated when the actual resistance values at the sender's side and the receiver's side differ. Then the second order equation yields the two resistance values but the eavesdropper is unable to determine the actual locations of the resistors and to find out the state of the sender's bit. The receiver knows that the sender has the inverse of his bit, similarly to quantum entanglement. The eavesdropper can decode the message if, for each bits, she inject current in the wire and measures the voltage change and the current changes in the two directions. However, in this way she gets discovered by the very first bit she decodes. Instead of thermal noise, proper external noise generators should be used when the communication is not aimed to be stealth.The manuscript was featured in the Science magazine, VOL 309, p. 2148 (2005, September 30)
I'll begin by giving a quick introduction to coding theory (in particular, I'll make sure I define all terminology) and then will describe how algebraic geometry enters the picture. Finally, I'll discuss a very simple geometric object called a complete intersection, and show how theoretical tools can be used to obtain information about how "good" the associated code is.The talk will be at a general level, i.e., I'll assume no prior knowledge of any words that occur in the title or this abstract.
A new approach to quantum searching is put forth which uses the quantum Fourier transform to deterministically and efficiently extract an unknown phase kernel stored globally in a database. Comparisons will be made to the Grover and Deutsch-Josza algorithms. Application of the Fourier search to complexity theory is still an open problem. We discuss a concrete physical realization of the algorithm in cavity quantum electrodynamics, where the the oracle query consists of a single atom traversing \log_2 N cavities, and the common time of passage through each cavity is determined to exponential precision with only polynomial overhead.
We define a generalized observable to be any operator on an n-dimensional Hilbert space that lies in the similarity class of a self-adjoint operator. For each such observable, we design a space of quantum-mechanical states amenable to the measurement of that observable. The ingredients of our construction are the Schmidt representation of a correlation and the employment of three-fold maximal entanglement in a quantum teleportation Gedanken experiment.
The anyonic quantum computer is based on the fractional quantum Hall effect (FQHE). Its design is known to have greatly reduced decoherence effects. In this talk, we will introduce such effects, and show their connections with topological quantum computing such as braiding and knot theory.
A new communication scheme is proposed where the signal energy put in the information channel is zero. The information is communicated via the parametric modulation of the fundamental classical and quantum fluctuation processes in the channel. This is the most hidden way of communication. Arrangements are proposed to make it absolutely secure, which means that the eavesdropper is discovered as soon as she extracts a single bit of information.
Spring 2005
We discuss new results about classical nonbinary BCH codes. We investigate BCH codes that have a small designed distance and determine the dimension and the true minimum distance of the code (up to 1). We settle the question when such codes contain their euclidean or hermitian duals, and derive the associated quantum stabilizer codes.Mathematics Frontiers Lecture Series - ColloquiumThis is joint work with Andreas Klappenecker and Pradeep Kiran Sarvepalli.
Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, rstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational e ort. I will provide a brief overview of the search for operational security criteria of quantum key distribution and discuss new trends in quantum cryptography.
The theory of classical universal computation was laid down in 1936, was implemented within a decade, became commercial within another decade, and dominated the world's economy half a century later. Quantum information technology is a fundamentally new way of harnessing nature. It is too early to say how important a way this will eventually be, but we can reasonably spec- ulate about its impact on computation and data security. Quantum computers use the quantum interference of di erent computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identi ed when quantum computation is viewed as multi-particle interference. I will use this approach to review the theory of quantum computation and its role in cryptanalysis.
In early 1935, Albert Einstein, together with Boris Podolsky and Nathan Rosen, published a classic paper which questioned the completeness of quantum mechanical description of reality and, in a tacit way, introduced quantum entanglement. After playing a signi cant role in the development of the foundations of quantum mechanics, entanglement has been recently rediscovered as a new physical resource with potential commercial applications. In particular it can be used to construct new methods of secure communication and new methods of breaking ciphers. I will outline the evolution of the concept from its origin till today and describe some of its current applications in quantum cryptography and quantum computation.
There is an intimate link between atomic coherence and quantum entanglement. Here we shall elucidate this link through an example where two thermal fields are entangled via atomic coherence.
Time and location: En/Ph 202, 2:00pm
When qubit dynamics contains imperfect operations due to, e.g., dephasing, instability in 2-level systems or a leaky cavity, it is no longer possible to describe the quantum systems in terms of ``pure states''. A more general class of Hilbert space operators is needed. For the purpose of quantum computing that class of operators corresponds to density matrices that are Hermitian and positive-semidefinite on a relevant finite dimensional Hilbert space. From where, one can discuss fidelity, the von Neumann equation, the Kraus Representation Theorem and the master equation. We will then show several examples of applications of this theory to instability in 2-level systems and leaky cavities.
Alice has tricked the King in the previous two problems by keeping atoms in her lab that were entangled with the state of the atom that the King was measuring. Furious with anger at this trickery, the King arrested Alice once again and gave her a new challenge. She has to prepare a quantum state of her own liking involving three silver atoms. The three atoms have to be handed over to the King and she would not be allowed to have any quantum state left in her possession which could be entangled with the three atoms. Then the King picks an arbitrary one of these atoms and measures it in one of the three spin components. Subsequently, the atoms are returned to Alice who is allowed to perform one experiment on them. Afterwards, the King reveals which atom has been measured in which spin component, and Alice has to immediately answer with the correct outcome or she will die an even more cruel death.The problem is significantly harder than the previous ones. We show how this and much more general problems can be solved with the help of a general theory based on the representation of affine resolvable designs by spherical codes.
The talk is based on joint work with Martin Rötteler.
The notorious mean king has captured Alice once again. Alice has to solve the King's new problem or she will face a cruel death. Will she live up to the challenge?We describe the problem and an elegant solution based on finite affine planes.
This is joint work with Martin Rötteler.
Slides Second Mean King's Problem,
Background: New Tales of the Mean King (CPSC 681 Seminar, 11/22/2004).
I will describe the route that took us from experimental work on a new packing problem (looking for "codes" in Grassmann manifolds - e.g., how should you place 18 planes through the origin in Euclidean 4-space so that they are as far apart as possible?) to the construction of codes for quantum computers. This work began as a project with Ron Hardin and John Conway, but many others (Peter Shor, Rob Calderbank, Eric Rains, Gabriele Nebe, ...) have since been involved. There are also applications to medicine, to visualizing multi-dimensional data, and to wireless communications.
The On-Line Encyclopedia of Integer Sequences (OEIS) is a database of number sequences that enables users to check if a sequence that has arisen in their work can been studied by others. A typical entry gives the first 50 or so terms of the sequence, formulae, references, links, computer programs for producing the sequence, etc.The OEIS has just reached 100,000 sequences and gets over 20,000 hits per day. Over ten thousand new sequences were added in the past year. This talk will discuss some classical sequences like Recaman's, some recent discoveries (like the "dismal primes"), and some unexpected connections between apparently unrelated sequences. Many open problems will also be mentioned.
We construct nonbinary quantum codes from classical generalized Reed-Muller codes and derive the conditions under which these quantum codes can be punctured. We provide a partial answer to a question raised by Grassl, Beth and Roetteler on the existence of q-ary quantum MDS codes of length n with q <= n <= q^2-1.This is joint work with Andreas Klappenecker.
The Quantum Computing Seminar is supported by the Telecommunications and
Informatics Task Force of Texas A&M University, and by the National Science
Foundation. Back to Andreas
Klappenecker's home page.