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Quantum random walks  an introductory overview
 Contemporary Physics
, 2003
"... This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physica ..."
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Cited by 191 (3 self)
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This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counterintuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from
Feedback Control of Quantum State Reduction
, 2004
"... Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for th ..."
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Cited by 73 (5 self)
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Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
Mutually Unbiased Bases are Complex Projective 2Designs
 PROC. 2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY
, 2005
"... Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for system of prime power dimension d, it is unknown whether this bound can be achieved for any nonpri ..."
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Cited by 31 (0 self)
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Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for system of prime power dimension d, it is unknown whether this bound can be achieved for any nonprime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2designs with angle set {0, 1/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2designs with angle set {1/(d+1)}.
Quantum control theory and applications: A survey
 IET Control Theory & Applications
, 2010
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Reconciliation of a QuantumDistributed Gaussian Key
, 2001
"... Two parties, Alice and Bob, wish to distill a binary secret key out of a list of Gaussian variables that were distributed with the help of quantum cryptography. We present a novel construction that allows the legitimate parties to get equal strings out of correlated variables, using a classical chan ..."
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Cited by 26 (3 self)
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Two parties, Alice and Bob, wish to distill a binary secret key out of a list of Gaussian variables that were distributed with the help of quantum cryptography. We present a novel construction that allows the legitimate parties to get equal strings out of correlated variables, using a classical channel, with as few leaked information as possible. This opens the way to securely correcting nonbinary key elements. In particular, the construction is refined to the case of Gaussiandistributed variables as it applies directly to a quantum cryptography protocol developed recently.
A.�Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow single photons
 Version 2.0 17 April 2, 2004 6.5 Optical Quantum Computing Summary
, 2000
"... Two light pulses propagating with ultraslow group velocities in a coherently prepared atomic gas exhibit dissipationfree nonlinear coupling of an unprecedented strength. This enables a singlephoton pulse to coherently control or manipulate the quantum state of the other. Processes of this kind re ..."
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Cited by 21 (1 self)
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Two light pulses propagating with ultraslow group velocities in a coherently prepared atomic gas exhibit dissipationfree nonlinear coupling of an unprecedented strength. This enables a singlephoton pulse to coherently control or manipulate the quantum state of the other. Processes of this kind result in generation of entangled states of radiation field and open up new prospectives for quantum information processing. PACS numbers 42.50.p, 42.65.k, 42.50.Dv,03.67.a Typeset using REVTEX 1 It has been known for more than thirty years that light fields or photons can interact with each other in atomic media much like massive particles do [1]. However, the strength of the interaction of two single light quanta is typically extremely weak. As a result, conventional nonlinear optics is feasible only when powerful laser beams, containing a large number of photons, interact in nonlinear materials. This Letter describes a method that allows for two slow light pulses [2–4] of tiny energies
The physics of forgetting: Landauer’s erasure principle and information theory
 Contemporary Physics
, 2001
"... This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyse Landauer ’ s principle which states that the erasure of information is ..."
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Cited by 19 (0 self)
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This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyse Landauer ’ s principle which states that the erasure of information is
Quantum estimation and the quantum central limit theorem
 Bulletin of the Mathematical Society of Japan
, 2003
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BoseEinstein Condensation
, 1995
"... Dispersive propagation of ultraslow light in an atomic ..."
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Cited by 15 (0 self)
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Dispersive propagation of ultraslow light in an atomic