arXiv subjects

David Poulin

Publications and source records attributed to David Poulin.

At least 73 records · Page 4Linked to original sources

arXiv2007

Quantum reference frames and deformed symmetries

In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system undergoes an unavoidable measurement "back-action" that modifies its properties. In a quantum-gravitational setting, it has been argued that such a back-action may produce effects that are described at an effective level as a form of deformed (or doubly) special relativity. We examine this possibility using a simple constrained system that has been extensively studied in the context of quantum information. While our conclusions support the idea of a symmetry deformation, they also reveal a host of other effects that may be relevant to the context of quantum gravity, and could potentially conceal the symmetry deformation.

gr-qc↗

arXiv2007

The structure of preserved information in quantum processes

We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every IPS is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrodinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.

quant-ph↗

arXiv2007

Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.

quant-ph↗

arXiv2007

Dynamics of a Quantum Reference Frame

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles.

quant-ph↗

arXiv2007

Optimal and Efficient Decoding of Concatenated Quantum Block Codes

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performance of the message passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message passing algorithms in two respects. 1) Optimal decoding increases by as much as 94% the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel. 2) For noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead.

quant-ph↗

arXiv2006

Stabilizer Formalism for Operator Quantum Error Correction

Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of standard quantum error correction theory. This is achieved by adding a "gauge" group to the standard stabilizer definition of a code that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 4 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.

quant-ph↗

arXiv2006

Operator quantum error correction

This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques - i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method - as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of ``unitarily noiseless subsystems''.

quant-ph↗

arXiv2005

Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe

We study the role of the information deposited in the environment of an open quantum system in course of the decoherence process. Redundant spreading of information -- the fact that some observables of the system can be independently ``read-off'' from many distinct fragments of the environment -- is investigated as the key to effective objectivity, the essential ingredient of ``classical reality''. This focus on the environment as a communication channel through which observers learn about physical systems underscores importance of quantum Darwinism -- selective proliferation of information about ``the fittest states'' chosen by the dynamics of decoherence at the expense of their superpositions -- as redundancy imposes the existence of preferred observables. We demonstrate that the only observables that can leave multiple imprints in the environment are the familiar pointer observables singled out by environment-induced superselection (einselection) for their predictability. Many independent observers monitoring the environment will therefore agree on properties of the system as they can only learn about preferred observables. In this operational sense, the selective spreading of information leads to appearance of an objective ``classical reality'' from within quantum substrate.

quant-ph↗

arXiv2005

Toy Model for a Relational Formulation of Quantum Theory

In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

quant-ph↗

arXiv2005

Algebraic and information-theoretic conditions for operator quantum error-correction

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum error-correction, decoherence-free subspaces, and noiseless subsystems. This paper develops (a) easily applied algebraic and information-theoretic conditions which characterize when operator quantum error-correction is feasible; (b) a representation theorem for a class of noise processes which can be corrected using operator quantum error-correction; and (c) generalizations of the coherent information and quantum data processing inequality to the setting of operator quantum error-correction.

quant-ph↗

arXiv2005

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

quant-ph↗

arXiv2005

Comment on "Some non-conventional ideas about algorithmic complexity"

We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater than that of the entire list. We show that this statement, although perplexing, is not as paradoxical as it seems when the definition of algorithmic complexity is applied correctly.

cs.CC↗

arXiv2004

A Unified and Generalized Approach to Quantum Error Correction

We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We arrive at the unified approach, which incorporates the known techniques -- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method -- as special cases, by combining active error correction with this generalized noiseless subsystem method. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.

quant-ph↗

arXiv2004

Objective properties from subjective quantum states: Environment as a witness

We study the emergence of objective properties in open quantum systems. In our analysis, the environment is promoted from a passive role of reservoir selectively destroying quantum coherence, to an active role of amplifier selectively proliferating information about the system. We show that only preferred pointer states of the system can leave a redundant and therefore easily detectable imprint on the environment. Observers who--as it is almost always the case--discover the state of the system indirectly (by probing a fraction of its environment) will find out only about the corresponding pointer observable. Many observers can act in this fashion independently and without perturbing the system: they will agree about the state of the system. In this operational sense, preferred pointer states exist objectively.

quant-ph↗

arXiv2004

Macroscopic Observables

We study macroscopic observables defined as the total value of a physical quantity over a collection of quantum systems. We show that previous results obtained for infinite ensemble of identically prepared systems lead to incorrect conclusions for finite ensembles. In particular, exact measurement of a macroscopic observable significantly disturbs the state of any finite ensemble. However, we show how this disturbance can be made arbitrarily small when the measurement are of finite accuracy. We demonstrate a tradeoff between state disturbance and measurement coarseness as a function of the size of the ensemble. Using this tradeoff, we show that the histories generated by any sequence of finite accuracy macroscopic measurements always generate a consistent family in the absence of large scale entanglement, for sufficiently large ensembles. Hence, macroscopic observables behave "classically" provided that their accuracy is coarser than the quantum correlation length-scale of the system. The role of these observable is also discussed in the context of NMR quantum information processing and bulk ensemble quantum state tomography.

quant-ph↗

arXiv2003

Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect

We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation, so for those maps admitting an efficient gate decomposition, it provides an exponential speed up over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of quantum chaos. Our result also illustrates the role of chaos in the process of decoherence.

quant-ph↗

arXiv2003

Estimation of the Local Density of States on a Quantum Computer

We report an efficient quantum algorithm for estimating the local density of states (LDOS) on a quantum computer. The LDOS describes the redistribution of energy levels of a quantum system under the influence of a perturbation. Sometimes known as the ``strength function'' from nuclear spectroscopy experiments, the shape of the LDOS is directly related to the survivial probability of unperturbed eigenstates, and has recently been related to the fidelity decay (or ``Loschmidt echo'') under imperfect motion-reversal. For quantum systems that can be simulated efficiently on a quantum computer, the LDOS estimation algorithm enables an exponential speed-up over direct classical computation.

quant-ph↗

arXiv2003

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of the system under study. This is a square root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

quant-ph↗