Capacities of Quantum Channels [PDF] [MP3] [M3U] Peter Shor AT&T |
We survey what is known about the information transmitting capacities of quantum channels, and address the question: How much information is contained in a quantum state? |
Prospects for Quantum Computation [PDF] [MP3] [M3U] David DiVincenzo IBM T. J. Watson Research Center divince@watson.ibm.com |
A "standard model" for the physical implementation of a quantum computer was laid out some years ago. It indicated a set of capabilities that had to be achieved to make quantum processing possible: 1) systems with well-characterized qubits must be constructed. 2) These qubits should be initializable to the "0" state. 3) It must be possible to control the one- and two-qubit Hamiltonian of the system, so that unitary quantum logic gates are enacted. 4) Decoherence and imprecision of gate operations must be kept very low. 5) Reliable measurements of the quantum state of individual qubits must be possible. In this talk I will indicate progress towards these goals, with examples from both the AMO and solid state world. |
Exponential Algorithmic Speedup by Quantum Walk [MP3] [M3U] Edward Farhi MIT farhi@mit.edu |
I will present an oracular problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on continuous time quantum walk which can used to solve our problem by rapidly traversing a graph. I will also show that no classical algorithm can solve this problem in subexponential time. |
State Randomisation: One Bit is Enough - and Why This is Interesting [PDF] [MP3] [M3U] Andreas Winter University of Bristol, Department of Computer Science winter@cs.bris.ac.uk |
I will discuss the problem of state randomisation by unitaries: contrary to the exact case, where 2 random bits per qubit are necessary and sufficient, allowing almost perfect randomisation requires only 1 bit per qubit asymptotically. This has many consequences: we can use this result to prove that remote state preparation is possible with 1 cbit and 1 ebit per qubit, to exhibit private quantum channels which require only 1 key bit per encrypted qubit, to improve the efficiency of quantum data hiding schemes, and to show that entanglement-assisted channel tomography can be exponenti-ally better than the unassisted case. A thorough discussion of the properties of the scheme is provided, especially contrasting it with previous work. (This is joint work with C H Bennett, P Hayden, D Leung and P W Shor.) |
Quantum Correlations and Thermodynamics [MP3] [M3U] Pawel Horodecki Techniczal University of Gdansk |
No Abstract Available |
Quantum Reverse Shannon Theorem [PDF] [MP3] [M3U] Charles H. Bennett IBM |
(Joint work with Igor Devetak, Aram Harrow,
Peter Shor, and Andreas Winter)
Reversing the usual direction of simulation, the QRST says that noiseless quantum channels can efficiently simulate noisy ones, in the presence of shared entanglement between sender and receiver. The theorem has long been known to hold for some channels on all sources, and about a year ago Shor showed that it holds for all channels on known IID sources. Recently Devetak and Winter have extended the latter result to include all separable sources, known or unknown. Whether the QRST holds for all channels on nonseparable sources remains open. |
Modular Functors and Quantum Codes [MP3] [M3U] Alexander Kirillov SUNY, Stony Brook kirillov@math.sunysb.edu |
This is an expository talk. A brief overview of the notion of modular functor, the main example (quantum sl(2)) and its use for quantum error-correcting codes, following the ideas of Freedman and Kitaev, will be given. |
Geometric Quantum Computation and Decoherence [PDF] [MP3] [M3U] Vlatko Vedral Imperial College London v.vedral@imperial.ac.uk |
In the first part of the talk I will introduce the basic theory behind geometric phases in quantum mechanics. The subject is presented in a general way so as to illustrate its wide applicability. In the second part, I will show how to perform any quantum computation using only geometric effects. It is then discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computation. I will calculate the geometric phase associated with the evolution of a system subjected to decoherence. Two main source of decoherence are considered: dephasing and spontaneous emission. I will demonstrate that the geometric phase is completely insensitive to the former case, but this is by no means true in deneral. Ways of combating general errors will be discussed at the end of the talk. |
Security of Quantum Key Distribution with Imperfect Devices [PDF] [MP3] [M3U] Hoikwong Lo University of Toronto hklo@comm.utoronto.ca |
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We estimate the key generation rate in some special cases: sources that emit weak coherent states, detectors with basis-dependent efficiency, and misaligned sources and detectors. |
Quantum Computation and Communication using Spin Chains [PDF] [MP3] [M3U] Sougato Bose Institute for Quantum Information, Caltech sbose@cs.caltech.edu |
I will discuss a protocol for quantum computation using a Heisenberg spin-chain with "untunable" couplings. This opens up the way for quantum computation using inhomogeneous magnetic fields on a 1D magnet. I will also discuss a few protocols for using a spin chain (a 1D magnet) as a channel for quantum communications, simply by inserting it between a sender and a receiver spin. No access to individual spins of the chain, nor any modulation by external fields will be required. This will be relevant for short distance quantum communications between two quantum processors. |
Universal Control of Quantum Subspaces and Subsystems [PDF] [MP3] [M3U] Paolo Zanardi Massachusetts Institute of Technology zanardi@paradosso.mit.edu |
I will describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems will be stated. Implications for quantum information processing will be briefly discussed. |
Universal Quantum Interfaces [PDF] [MP3] [M3U] Andrew Landahl MIT alandahl@mit.edu |
(Joint work with Seth Lloyd and Jean-Jacques Slotine.)
To observe or control a quantum system, one must interact with it via an interface. In this talk I present simple universal quantum interfaces---quantum input/output ports consisting of a single qubit that interacts with a system. I will show that under very general conditions the ability to observe and control the qubit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored. |
Limits on Gates with Trapped Ions. [PDF] [MP3] [M3U] Ignacio Cirac Max-Planck-Institut für Quantenoptik Ignacio.Cirac@mpq.mpg.de |
Trapped ions appear as one of the most promising system to implement quantum computations. So far, the basic steps to build a scalable quantum computer have been carried out. The current limitations are now in two-qubit quantum gates. In this talk we propose [1] a new method to perform such gates which does not require atom addressing, is valid for arbitrary temperature, and it is not limited in time by the oscillation frequency of the ions. I will also mention some recent work on the entanglement properties of spin chains [2]. |
Clean, Fast and Scalable Quantum Logic with Trapped Ions [PDF] [MP3] [M3U] Boris Blinov FOCUS Center and University of Michigan Department of Physics bblinov@umich.edu |
A collection of trapped atomic ions is an exciting candidate for a large-scale quantum computer, with high-fidelity quantum logic gates and perfect quantum state detection. Experiments with small numbers of atomic ion qubits have shown promising results [1,2]. The task now is to scale the size of a trapped-ion quantum register to many qubits. I will discuss two radically different approaches studied experimentally by our group, including the "quantum CCD" scheme [3] and strong-field dipole force quantum logic gates [4,5]. These two methods bypass the necessity to cool all the qubit ions to the ground state of motion and individually address each ion. In a "quantum CCD" processor, the qubit ions are stored individually in an array of tiny interconnected traps and are shuttled to an interaction region by electric fields for pair-wise entanglement. I will report on progress in the fabrication of ion trap arrays for quantum CCD operation. The second method relies on pushing of the qubit ions with electric field gradients of high-intensity laser pulses. Here, the gate time is not limited by the ions' motion in the trapping potential (order of 1 us), and thus can in principle be very fast. Our initial pulsed laser experiments are conducted with Cd+ ions confined in an asymmetric rf quadrupole trap. The dipole force is provided by 10 ns pulses from a frequency-quadrupled Nd:YAG laser at 266nm. I will report on first results in pushing laser-cooled ions with this laser, and the prospects of applying spin-dependent forces for future entangling logic gates in this system. |
Quantum Computation with Neutral Atoms and (Artificial) Ions [PDF] [MP3] [M3U] Tommaso Calarco NIST Tommaso.Calarco@nist.gov |
I will describe and compare several recent proposals for implementing quantum gates via quantum optical methods in atomic systems and quantum dots. More specifically, I will review schemes based on ions (using electrostatic interactions), quantum dots (using dipole-dipole interactions) and neutral atoms (using cold collisions and molecular interactions), discussing decoherence sources and ways to circumvent their effects. |
Quantum Information Processing with Trapped Ultracold Atoms [PDF] [MP3] [M3U] Ivan Deutsch University of New Mexico ideutsch@info.phys.unm.edu |
Neutral atoms are natural candidates as the keepers of quantum information given their weak coupling to the environment and the rapid advances in laser cooling and trapping technology. Many tools for building a rudimentary quantum computer are currently or nearly in place ? state preparation through optical pumping, coherent control through laser/rf spectroscopy, measurement through monitored quantum jumps. In order to make progress towards the ultimate goal, we must focus attention on laboratory development of these control tools, must crucially two-qubit quantum logic gates. For atoms, this is effectively the problem of coherent control of a dimer. This is the newest ingredient beyond that common employed in atomic clocks and analogous systems. Optical lattices provide an excellent arena in which to begin implementing these building blocks, with promise of scalability and parallelism necessary for ultimate fault-tolerant operation. |
Quantum Feedback in Cavity QED [PDF] [MP3] [M3U] Luis Orozco SUNY, Stony Brook Luis.Orozco@sunysb.edu |
Measurements of quantum optical correlations on the light emitted by a cavity QED system permit the study of its conditional dynamics and the modification, via quantum feedback, its conditional state.
Work done in collaboration with M. L.. Terraciano, F. M. Dimler, W. P. Smith and J. E. Reiner and supported by NSF and NIST. |
Programmable Quantum Circuits [PDF] [MP3] [M3U] Mark Hillery Hunter College of CUNY mhillery@hunter.cuny.edu |
Single-purpose quantum circuits have been designed for such tasks as approximate cloning and qubit inversion. More recently programmable circuits, whose effect on an input quantum state is controlled by a program state have been studied. Some examples of programmable circuits will be presented, and general properties of such circuits will be discussed. |
Reciprocal Gates: How to Enforce an Action--Reaction Principle for Information [PDF] [MP3] [M3U] Tommaso Toffoli Boston University tt@bu.edu |
Logic primitives such as the so-called "Toffoli gate", which is invertible in
its classical version and unitary in its quantum version, are meant to
capture one essential aspect of physics, namely, microscopic reversibility,
and thus conservation of fine-grained entropy. However, primitives of this
kind still represent a significant departure from microscopic physics insofar
as they do not satisfy an "action--reaction" principle: the controlled signal
c influences the controlled signal x but is not influenced by it. (Imagine c
to represent a hard wall and x a ball bouncing off it. Clearly c influences
x. However, for c not to be influenced by x we have to imagine an infinitely
massive wall---a somewhat unrealistic idealization.)
We define "reciprocal logic gates" in both classical and quantum context. In addition to invertibility, these obey the following "action--reaction" criterion (assume for simplicity two inputs, x and y, and two outputs, x' and y'): The mutual information between x and y' conditional on y equals the mutual information between y and x' conditional on x. Intuitively, the "amount of influence" of signal x on y must equal that of signal y on x. We discuss the existence of nontrivial reciprocal gates, the preservation of reciprocity on composition of such gates, and their computation universality. In conclusion, like the invertibility constraint, this additional physically-motivated criterion further restricts the structure of networks capable of useful computation, but (unlike the linearity constraint) does not arrive to "kill" computation universality. In sum, there is still room to make logic primitives closer to physics. |
Information and Irreversibility of Quantum Measurement. [PDF] [MP3] [M3U] Lev B. Levitin Boston University, ECE Department levitin@bu.edu |
The paper gives a historical review of the interconnections between quantum information theory and quantum theory of measurement. A measurement is necessary to obtain information, but any measurement, in general, introduces irreversibility in the time evolution of a quantum system. This is true for both direct (von Neumann)and indirect (POVM)measurements. This fundamental property of the quantum world results in "splitting" of the classical measure of information (in terms of the entropy of physical ensembles)into two unequal quantities: information (in Shannon's sense)and entropy defect, those quantities being related by an inequality, rather than equality. This fact has important physical implications in relation to the classical problem about the amount of heat convertable into work in the process of relaxation of a non-equilibrium system. It is also remarkable that for a system with infinite-dimensional Hilbert space POVM measurements cannot provide more information than direct measurements. However, it has been shown later that the entropy defect limit can be attained asymptotically for an infinitely long process of information transmission. The information- theoretical meaning of some specifically quantum phenomena, such as no-cloning theorem and "superdense coding" is also discussed. |
Reversible Computing: Quantum Computing's Practical Cousin [PDF] [MP3] [M3U] Michael Frank University of Florida CISE Dept. mpf@cise.ufl.edu |
Barring major algorithmic advances, coherent quantum computing using superposition states is known to offer polynomial to exponential speedups for only a few specialized classes of problems. Despite this limited usefulness, fault-tolerant quantum computing is very difficult to achieve. Another approach is both easier, and more useful. Suppose we don¡¦t use superpositions explicitly in our algorithms, but instead restrict the quantum state trajectory to paths that consist (as in classical computing) of only direct transitions between computational basis states. These basis states can then be chosen to be any convenient set of pointer states within whatever decoherence-free subspace happens to be naturally super-selected by the measurement observable induced by the system¡¦s built-in parasitic interactions with its environment, and so, as a result, these states are naturally very stable, and require only classical forms of error correction.
However, even in this highly restricted (and much more easily implemented) special case of quantum computing, we can still show that a ballistic (self-contained, and still mostly coherent) variation of the scheme still in fact provides polynomial cost-efficiency advantages for most general-purpose computations, excluding only the small minority of tasks that are either totally serial, or totally parallelizable and very loosely-coupled. This general advantage is due simply to the near-reversibility (low rate of entropy generation) in the ballistic evolution of a well-isolated quantum system. Given the existence of both fundamental and practical bounds on attainable entropy flux densities, the improved entropic efficiency can be demonstrated to boost theoretical performance on, in fact, the majority of computational applications that require tightly-coupled parallelism. Because of the generality of this advantage, we can even argue that this approach, called reversible computing, can reasonably be anticipated to have a greater overall practical economic impact than the more difficult, full-quantum approach, which presently appears somewhat more limited in its potential applications. In this talk, I will outline the basic technological and architectural requirements for reversible computing, and show how to analyze and optimize the system-level cost-efficiency gains that can be attained using this approach. Given the raw decoherence rate of a particular device mechanism, I show how to optimize other design parameters including the redundancy factor (physical qubits per logical bit) of the logic encoding, the speed of the logic transitions, and the degree of logical reversibility of an arbitrary target computation emulated using Bennett¡¦s spacetime-efficient algorithm. With these parameters simultaneously optimized, I show that improvements in cost-efficiency on the order of 1,000„e that of contemporaneous irreversible computing can be projected for general-purpose desktop-scale applications by the middle of the century. I also discuss particular technological strategies for implementing the requirement of ballistic, self-contained evolution, which is not a requirement for traditional quantum algorithms, which place no limits on dissipation in the control system. I will also demonstrate a simple new mechanical model of self-timed, 3D, ballistic computation that avoids a variety of defects that were present in earlier models of reversible computing. |
Reversible Josephson-Junction Circuits with SQUID based Gates [PDF] [MP3] [M3U] Vasili Semenov SUNY, Stony Brook Vasili.Semenov@StonyBrook.edu |
Authors: Vasili Semenov, Geoge Danilov, and Dmiti Averin,
It has been known for a long time that the thermodynamic limit kBTln2 on the energy dissipation per logic operation can be overcome by physically and logically reversible circuits. However, explicit experimental demonstration of this is still lacking, and would be highly desirable both in its own right and in view of strong interest in inherently reversible quantum computation. In this work, we analize a few gates including ``negative-inductance SQUID``, that are suitable for the experimental demonstration of reversible information processing in Josephson-junction circuits, and present results of its theoretical and experimental analysis. |
Unconditionally Secure Quantum Bit Commitment [PDF] [MP3] [M3U] Horace Yuen Northwestern University yuen@ece.northwestern.edu |
Four different types of unconditionally secure quantum bit commitment protocols will be described together with their security proofs, amid a discussion of the limited scope of the "impossilibity proof". |
Spatial Search by Quantum Walk [PDF] [MP3] [M3U] Andrew Childs MIT amchilds@mit.edu |
Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log(N)) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph reproduces the continuous time search algorithm of Farhi and Gutmann, and other previously known results show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk algorithm takes time of order sqrt(N) poly(log(N)), and in d<4, the algorithm provides no speedup. |
Distilation of Secret Key and Entanglement from Quantum States [PDF] [MP3] [M3U] Andreas Winter University of Bristol winter@cs.bris.ac.uk |
No abstract available. |
A Q_phase=25000 Superconducting Charge-Phase Qubit. [PDF] [MP3] [M3U] Michel Devoret Yale University michel.devoret@yale.edu |
We have designed and operated a superconducting tunnel junction circuit that behaves like a two-level quantum system (qubit). The circuit consists of a single Cooper pair transistor in parallel with a large current-biased Josephson junction. One-qubit rotations are performed by microwave voltage pulses applied to the gate of the Cooper-pair transistor. The qubit is readout by a radio-frequency current pulse applied to the large junction. Depending on the state of the qubit, this junction switches or not to its voltage state, an event which is easily detected. All manipulations of the qubit can take place at a working point where the transition energy is insensitive to small fluctuations in bias parameters. By performing a Ramsey fringe experiment at this optimum bias point, we have measured a quantum coherence quality factor Q_phase=25000. |
Demonstration of Rabi Oscillations in a Josephson Tunnel Junction [PDF] [MP3] [M3U] Siyuan Han University of Kansas han@ku.edu |
Josephson junctions (JJ) with very low damping behave quantum mechanically. The Hamiltonian of a current bised JJ is equivalent to that of a particle in a tilted washboard potential that has a series of potential wells. For a JJ initially trapped in one of these wells, the energy is quantized and the level spacing between the ground state and the first excited state is typically around 10 GHz. The quantum state of a JJ then can be manipulated by the application of microwave pulses that result in Rabi oscillations. Because the rate of tunneling out of the potential well from the first excited state is about 103 higher than that from the ground state, the JJ's state can be readout by measuring its tunneling rate. Furthermore, decoherence time can also be extracted by watching how fast the amplitude of the Rabi oscillations decays. By carefully isolating a NbN/AlN/NbN Josephson tunnel junction from its electromagnetic environment, we observed Rabi oscillations. The decoherence time obtained from this measurement is about 5 ms the longest observed in any solid-state qubit so far. |
Controlled Coupling of Charge Qubits [PDF] [MP3] [M3U] Dmitri Averin SUNY, Stony Brook |
No Abstract Available |
Capacitively Coupled Josephson-Junction Qubits [PDF] [MP3] [M3U] Philip R. Johnson Department of Physics, University of Maryland College Park |
Co-Authors: Frederick W. Strauch, Alex J. Dragt,
Department of Physics, University of Maryland College Park.
A single current biased Josephson junction (CBJJ) is a promising candidate for a solid-state superconducting qubit. The effective coupling strength of two (or more) capacitively coupled CBJJ's may be actively controlled by varying each junction's applied bias current, thus bringing the junctions in or out of resonance. Active tuning of the coupling of qubits provides a powerful mechanism for manipulating quantum states. We numerically compute the energy levels and macroscopic quantum states of the nonlinear coupled-qubit Hamiltonian to guide the engineering of this coupled qubit system. Necessary for the challenge of high fidelity quantum computing, our methods incorporate the effects of tunneling and higher energy states, including the continuum states. Recently, experimental evidence for the macroscopic quantum mechanics of this system in very close agreement with our numerical predications has been seen. |
Quantum Logic Gates for Capacitively Coupled Josephson Junction [PDF] [MP3] [M3U] Frederick W. Strauch Department of Physics, University of Maryland College Park |
Co-Authors: Philip R. Johnson, Alex J. Dragt,
Department of Physics, University of Maryland College Park
Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we have identified two fundamental (universal) two-qubit evolutions, equivalent to controlled-phase and swap gates. By design, these gates take advantage of extra states in the two-junction Hilbert space. Numerical solutions of the time-dependent Schroedinger equation demonstrate that these operations can be performed with good fidelity. |
Spin Based Quantum Information Processing [PDF] [MP3] [M3U] Daniel Loss University of Basel, Department of Physics daniel.loss@unibas.ch |
Spins of electrons offer the opportunity to store and manipulate phase coherence over length and time scales much larger than for charge, with promising applications in conventional and in quantum information processing [1,2]. The qubit is defined in terms of the spin of an electron, being localized in structures such as an atom, molecule, quantum dot etc. The desired manipulation of the spins (qubits), which includes single spin rotations, spin-spin interactions, and spin read-out, can be achieved by purely electric means in terms of gates which are externally controlled by voltage pulses (spin-charge-conversion). I discuss schemes for using a single quantum dot as a spin filter and spin read-out device [3], and show how the spin decoherence time can be measured in a transport set-up [4]. I address the issue of spin decoherence due to non-uniform hyperfine interactions with nuclei (being the dominant source of decoherence) and show that for electrons conned to dots the spin decay is non-exponential[5]. |
Spin Computation in Nanostructures [PDF] [MP3] [M3U] Sankar Das Sarma University of Maryland, Department of Physics dassarma@physics.umd.edu |
Electron (or nuclear) spin in semiconductor nanostructures has been projected as suitable qubits for quantum computation. Spins are stable two level systems with long coherence times. Single qubit manipulation is possible by applying external magnetic or radiation fields, and two-qubit controlled-not operations can be carried out by using the exchange coupling between different spins. I will review the current status of quantum computation using spins in semiconductor nanostructures, focusing on GaAs quantum dots and donors in Si. I will also briefly discuss olur recent idea of using quantum Hall pseudospins as qubits in the spontaneous interlayer coherent quantum phase. |
Coherent Control of Fractional Charges in Quantum Antidot Devices [PDF] [MP3] [M3U] Vadimir J Goldman SUNY, Stony Brook goldman@insti.physics.sunysb.edu |
A quantum antidot (QAD) electrometer has been used in the first direct observation of the fractionally quantized electric charge of Laughlin quasiparticles. In a parallel development, topological computation with Abelian and non-Abelian quasiparticles of two-dimensional interacting electron systems has been suggested as a way of implementing intrinsically fault-tolerant quantum computation. Topological computation employs a fractional statistical phase created by the transfer of one quasiparticle of the system around another to perform quantum logic. Such a phase is fixed by the topological properties of the system wavefunction and should be insensitive to environment-induced perturbations of the quasiparticle dynamics. The most thoroughly studied and realistic example of a two-dimensional system with fractional statistics of quasiparticles is provided by incompressible electron liquids of the fractional quantum Hall (FQH) effect.
I will review the basic physics of quantum antidots in the i=1 and f =1/3 QH states, and then discuss the experimental determination of the quasiparticle coherence time in a QAD ``molecule". The invariance of quasiparticle charge has been demonstrated in recent experiments. In these experiments, the Laughlin quasiparticle charge has been found to be e*=e/3 \pm 1.2%, independent of temperature, tunneling current and conductance in a wide range of experimental parameters. Thus our experimental results imply robustness of Laughlin quasiparticles localized on QADs, and we conclude that it is possible to control and manipulate fractional quasiparticles in QAD devices in a manner similar to electrons in quantum dots. The objective of future research is to study possibility of using the controlled transport of FQH quasiparticles in structures with multiple antidots to perform quantum logic operations. The most important question to be answered by the future work is to what extent the topological nature of the statistical phase of fractionally charged quasiparticles helps to alleviate the decoherence problem in quantum computation. The future research should result in a detailed understanding of topological quantum computation and should clarify issues relevant to its eventual practical implementation using FQH systems. |
Entanglement in Spin Chains [PDF] [MP3] [M3U] Rosario Fazio Scuola Normale Superiore fazio@sns.it |
I will discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. Entanglement can be classified in the framework of the scaling theory of phase transition. There is a profound differences between the classical correlations, whose correlation lenght diverges at the phase transition, and non-local quantum correlations that remain, in general, short ranged. In the last part of the presentation I will report on some results on the dynamics of entangled in spin chains. |
Entanglement in Quantum Critical Phenomena [PDF] [MP3] [M3U] Guifre Vidal California Institute of Technology vidal@iqi.caltech.edu |
A microscopic calculation of the ground-state entanglement in several spin-chain models shows the emergence of universal scaling behavior at a quantum phase transition. Critical entanglement, embracing the system at all length scales simultaneously, is thus controlled by conformal symmetry. Instead, away from the critical point quantum correlations are saturated by the appearance of a mass gap. This observation has stimulated the search for an efficient simulation of non-critical spin chains. |
Entanglement and Toeplitz Determinants [PDF] [MP3] [M3U] Vladimir Korepin C.N. Yang Institute for Theoretical Physics, SUNY, Stony Brook korepin@insti.physics.sunysb.edu |
We consider one-dimensional quantum spin chain, which is called isotropic XY model in a transverse magnetic field. We are interested in the case of zero temperature and infinite volume. We study the entanglement of a block L of neighboring spins with the rest of the system. We represent the entanglement in terms of a Toeplitz determinant and calculate the asymptotics. |
Geometric Measure of Entanglement [PDF] [MP3] [M3U] Tzu-Chieh Wei University of Illinois at Urbana-Champaign twei@uiuc.edu |
Authors: Tzu-Chieh Wei and Paul M. Goldbart (University of Illinois at
Urbana-Champaign)
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (Shimony [1] and Barnum and Linden [2]), is explored for bipartite and multipartite pure and mixed states. It is determined for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states [3,4]. The physical meaning of the geometric measure of entanglement is also investigated via connections with the notion of entanglement witnesses [5]. |
On the Ideal Quantum Random Number Generator [PDF] [MP3] [M3U] Viacheslav Belavkin University of Nottingham |
No Abstract Available |
Data Compression for a Class of Quantum Information Sources [PDF] [MP3] [M3U] Nilanjana Datta Centre for Mathematical Sciences, University of Cambridge n.datta@statslab.cam.ac.uk |
A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from a class of such sources and show that asymptotically it is given by the von Neumann entropy rate. Our result can be viewed as a quantum analogue of Shannon's noiseless coding theorem for a class of non - i.i.d. quantum information sources and an extension of Schumacher's coding theorem. |
Quantum Cellular Automata from Lattice Field Theories [PDF] [MP3] [M3U] Michael McGuigan Information Technology Division, Brookhaven National Laboratory mcguigan@bnl.gov |
We apply the methods of lattice field theories to the quantization of reversible cellular automata. We discuss spin and quantum dot cellular automata for their importance in experimental realizations and their use in quantum computation. We discuss the quantization five main categories of cellular automata: bosonic, fermionic and supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of Thorn and Bergman and represents a possible link of cellular automata theory to fundamental physics. Previous studies of quantum cellular automata utilize the wave function values as cell contents and the discretized linear Dirac equation as an update equation. We show that our approach to the quantization of fermionic cellular automata includes this utilization as a field equation, and in addition allows for nonlinearity through lattice field interactions. |
Thermodynamics of Fault-Tolerant Quantum Computation [PDF] [MP3] [M3U] Maxim Raginsky Northwestern University maxim@ece.northwestern.edu |
The present work, is concerned with formulating the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility of fault-tolerant quantum computation with constant error rate can be cast as a renormalization (block-spin transformation) of the site percolation process describing occurrence of errors during the computation. We also use this interpretation to characterize the trade-off between the complexity overhead of the fault-tolerant circuit and the threshold error rate. |
Operator-Schmidt Decompositions and the Fourier Transform, Applications to Schmidt-Numbers of Unitaries [PDF] [MP3] [M3U] Jon Tyson Harvard University jonetyson@post.harvard.edu |
We construct a family of unitaries on C^{n}xC^{n} whose operator-Schmidt decompositions are given by the discrete Fourier transform. As an application, we construct unitaries on C^{3}xC^{3} with operator-Schmidt numbers 1, 2, 3, 5, 6, 7, 8, and 9, providing a counter-example to a conjecture of Nielsen et al in "Quantum Dynamics as a physical resource," arXiv:quant-ph/0208077 v3, which will appear in Phys. Rev A. |
Practical Aspects of the QKD Security [PDF] [MP3] [M3U] Alexei Trifonov MagiQ Technologies |
We analyze the security of the QKD system based upon weak coherent pulse implementation. Special attention is paid to the single photon detector problem and limitation imposed by detector performance. Brief overview of physical security of the QKD system will be given. |