Quantum scattering theory on graphs with tails (2009)
Varbanov, Martin, Brun, Todd A.
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such...
Scheme for fault-tolerant holonomic computation on stabilizer codes (2009)
Oreshkov, Ognyan, Brun, Todd A., Lidar, Daniel A.
This paper generalizes and expands upon the work [Phys. Rev. Lett. 102, 070502 (2009)] where we introduced a scheme for fault-tolerant holonomic quantum computation (HQC) on stabilizer codes. HQC is...
Applications of the decoherence formalism (2009)
In this work the decoherence formalism of quantum mechanics is explored and applied to a number of interesting problems in quantum physics. The boundary between quantum and classical physics is...
Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding (2008)
We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional...
Localized closed timelike curves can perfectly distinguish quantum states (2008)
Brun, Todd A., Harrington, Jim, Wilde, Mark M.
We show that qubits traveling along closed timelike curves are a resource that a party can exploit to distinguish perfectly any set of quantum states. As a result, an adversary with access to closed...
Quantum Convolutional Coding with Shared Entanglement: General Structure (2008)
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless...
Protecting Quantum Information with Entanglement and Noisy Optical Modes (2008)
We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes,...
Operator quantum error correction for continuous dynamics (2008)
Oreshkov, Ognyan, Lidar, Daniel A., Brun, Todd A.
We study the conditions under which a subsystem code is correctable in the presence of noise that results from continuous dynamics. We consider the case of Markovian dynamics as well as the general...
Fault-tolerant holonomic quantum computation (2008)
Oreshkov, Ognyan, Brun, Todd A., Lidar, Daniel A.
We explain how to combine holonomic quantum computation (HQC) with fault tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of...
Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding (2008)
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to...
Hitting time for the continuous quantum walk (2008)
Varbanov, Martin, Krovi, Hari, Brun, Todd A.
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this...
Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes (2008)
Hsieh, Min-Hsiu, Brun, Todd A., Devetak, Igor
We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical...
Classical Enhancement of Quantum Error-Correcting Codes (2008)
Kremsky, Isaac, Hsieh, Min-Hsiu, Brun, Todd A.
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism...
Unified Quantum Convolutional Coding (2008)
We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather''...
Entanglement-Assisted Quantum Convolutional Coding (2007)
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to...
Test of weak measurement on a two- or three-qubit computer (2007)
Brun, Todd A., Diosi, Lajos, Strunz, Walter T.
Current quantum computer technology is sufficient to realize weak measurements and the corresponding concept of weak values. We demonstrate how the weak value anomaly can be tested, along with...
Coherent Communication with Linear Optics (2007)
Wilde, Mark M., Brun, Todd A., Dowling, Jonathan P., Lee, Hwang
We show how to implement several continuous-variable coherent protocols with linear optics. Noise can accumulate when implementing each coherent protocol with realistic optical devices. Our analysis...
Convolutional Entanglement Distillation (2007)
Wilde, Mark M., Krovi, Hari, Brun, Todd A.
We develop a theory of entanglement distillation that exploits a convolutional coding structure. We provide a method for converting an arbitrary classical binary or quaternary convolutional code into...
Entanglement-Assisted Quantum Error Correction with Linear Optics (2007)
Wilde, Mark M., Krovi, Hari, Brun, Todd A.
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary...
Continuous quantum error correction for non-Markovian decoherence (2007)
Oreshkov, Ognyan, Brun, Todd A.
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the...
Quantum walks on quotient graphs (2007)
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated...
Decomposing generalized measurements into continuous stochastic processes (2007)
Varbanov, Martin, Brun, Todd A.
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of...
A Matrix Factorization of Extended Hamiltonian Leads to $N$-Particle Pauli Equation (2007)
Reed, Irving S., Brun, Todd A.
In this paper the Levy-Leblond procedure for linearizing the Schr\"odinger equation to obtain the Pauli equation for one particle is generalized to obtain an $N$-particle equation with spin. This is...
Coherent Communication with Continuous Quantum Variables (2006)
Wilde, Mark M., Krovi, Hari, Brun, Todd A.
The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit...
Hypersensitivity and chaos signatures in the quantum baker's maps (2006)
Scott, A. J., Brun, Todd A., Caves, Carlton M., Schack, Ruediger
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for...
Quantum walks with infinite hitting times (2006)
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite....
Hypersensitivity and chaos signatures in the quantum baker's maps (2006)
Scott, Andrew James, Brun, Todd A, Caves, Carlton M, Schack, Rüdiger
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for...
Hypersensitivity and chaos signatures in the quantum baker's maps (2006)
Scott, Andrew James, Brun, Todd A, Caves, Carlton M, Schack, Rüdiger
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for...
Hypersensitivity and chaos signatures in the quantum baker's maps (2006)
Scott, Andrew James, Brun, Todd A, Caves, Carlton M, Schack, Rüdiger
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for...
Hitting time for quantum walks on the hypercube (2005)
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time...
Infinitesimal local operations and differential conditions for entanglement monotones (2005)
Oreshkov, Ognyan, Brun, Todd A.
Much of the theory of entanglement concerns the transformations that are possible to a state under local operations with classical communication (LOCC); however, this set of operations is complicated...
Weak measurements are universal (2005)
Oreshkov, Ognyan, Brun, Todd A.
It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized...
Measuring polynomial functions of states (2004)
In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $\rho$ can be determined by finding the expectation value of an observable on $m$ copies of...
Brun, Todd A., Goan, Hsi-Sheng
A requirement for many quantum computation schemes is the ability to measure single spins. This paper examines one proposed scheme: magnetic resonance force microscopy, including the effects of...
Probability in decoherent histories (2003)
The decoherent (consistent) histories formalism has been proposed as a means of eliminating measurements as a fundamental concept in quantum mechanics. In this formalism, probabilities can be...
Decoherence and quantum trajectories (2003)
Decoherence is the process by which quantum systems interact and become correlated with their external environments; quantum trajectories are a powerful technique by which decohering systems can be...
Quantum random walks with decoherent coins (2002)
Brun, Todd A., Carteret, Hilary A., Ambainis, Andris
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk...
Quantum Walks driven by many coins (2002)
Brun, Todd A., Carteret, Hilary A., Ambainis, Andris
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum...
Computers with closed timelike curves can solve hard problems (2002)
A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I...
The quantum to classical transition for random walks (2002)
Brun, Todd A., Carteret, Hilary A., Ambainis, Andris
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional...
How much state assignments can differ (2002)
The state that an observer attributes to a quantum system depends on the information available to that observer. If two or more observers have different information about a single system, they will...
Comment on "Quantum optimization for combinatorial searches" (2002)
Zalka, Christof, Brun, Todd A.
This is a comment on a recent publication claiming to have found a ``quantum optimization'' algorithm which outperforms known algorithms for minimizing some ``cost function''. Unfortunately, this...
How much state assignments can differ (2001)
Brun, Todd A., Finkelstein, J., Mermin, N. David
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
A simple model of quantum trajectories (2001)
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In...
Generalized stochastic Schroedinger equations for state vector collapse (2001)
Adler, Stephen L., Brun, Todd A.
A number of authors have proposed stochastic versions of the Schr\"odinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic...
Remotely prepared entanglement: a quantum web page (2001)
In quantum teleportation, an unknown quantum state is transmitted from one party to another using only local operations and classical communication, at the cost of shared entanglement. Is it possible...
Entanglement purification of unknown quantum states (2000)
Brun, Todd A., Caves, Carlton M., Schack, Ruediger
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of...
Schack, Ruediger, Brun, Todd A., Caves, Carlton M.
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on...
Parametrization and distillability of three-qubit entanglement (2000)
There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a...
Distillation of GHZ states by selective information manipulation (2000)
Methods for distilling maximally entangled tripartite (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique...
Coupling nanocrystals (quantum dots) to a high-$Q$ whispering gallery mode (WGM) of a silica microsphere, can produce a strong coherent interaction between the WGM and the electronic states of the...
Classical Dynamics of the Quantum Harmonic Chain (1999)
Brun, Todd A., Hartle, James B.
The origin of classical predictability is investigated for the one dimensional harmonic chain considered as a closed quantum mechanical system. By comparing the properties of a family of...
Entropy of Classical Histories (1998)
Brun, Todd A., Hartle, James B.
We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then...
Realizing the quantum baker's map on an NMR quantum computer (1998)
Brun, Todd A., Schack, Ruediger
By numerically simulating an implementation of the quantum baker's map on a 3-qubit NMR quantum computer based on the molecule trichloroethylene, we demonstrate the feasibility of quantum chaos...
Continuous measurements, quantum trajectories, and decoherent histories (1997)
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques corresponding to continuous measurement schemes,...
Effects of Noise on Quantum Error Correction Algorithms (1997)
Adriano Barenco, Todd A. Brun, Rudiger Schack, Timothy P. Spiller
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The...
Effects of noise on quantum error correction algorithms (1996)
Barenco, Adriano, Brun, Todd A., Schack, Ruediger, Spiller, Tim
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The...
Interference in dielectrics and pseudo-measurements (1996)
Brun, Todd A., Barnett, Stephen M.
Inserting a lossy dielectric into one arm of an interference experiment acts in many ways like a measurement. If two entangled photons are passed through the interferometer, a certain amount of...
From Quantum to Classical: the Quantum State Diffusion Model (1996)
Gisin, Nicolas, Brun, Todd A., Rigo, Marco
Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe...
A C++ library using quantum trajectories to solve quantum master equations (1996)
Schack, Ruediger, Brun, Todd A.
Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in...
Quantum jumps as decoherent histories (1996)
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its...
Quantum State Diffusion and Time Correlation Functions (1995)
In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master...
Quantum chaos in open systems: a quantum state diffusion analysis (1995)
Brun, Todd A., Percival, Ian C., Schack, Rüdiger
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to...
An Example of the Decoherence Approach to Quantum Dissipative Chaos (1995)
Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum...
Applications of the decoherence formalism (1994)
In this work the decoherence formalism of quantum mechanics is explored and applied to a number of interesting problems in quantum physics. The boundary between quantum and classical physics is...
The Decoherence of Phase Space Histories (1994)
In choosing a family of histories for a system, it is often convenient to choose a succession of locations in phase space, rather than configuration space, for comparison to classical histories....
Quantum Dissipative Chaos (1993)
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the...
Quasiclassical Equations of Motion for Nonlinear Brownian Systems (1993)
Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description....