arXiv subjects

Terry Rudolph

Publications and source records attributed to Terry Rudolph.

At least 91 records · Page 5Linked to original sources

arXiv2007

One-way quantum computation with four-dimensional photonic qudits

We consider the possibility of performing linear optical quantum computation making use of extra photonic degrees of freedom. In particular we focus on the case where we use photons as quadbits. The basic 2-quadbit cluster state is a hyper-entangled state across polarization and two spatial mode degrees of freedom. We examine the non-deterministic methods whereby such states can be created from single photons and/or Bell pairs, and then give some mechanisms for performing higher-dimensional fusion gates.

quant-ph↗

arXiv2007

Degradation of a quantum directional reference frame as a random walk

We investigate if the degradation of a quantum directional reference frame through repeated use can be modeled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading quantum directional reference frame, defined as the average probability of correctly determining the orientation of a test system, can be fit precisely using such a model. Physically, the mechanism for the random walk is the uncontrollable back-action on the reference frame due to its use in a measurement of the direction of another system. However, we find that the magnitude of the step size of this random walk is not given by our classical model and must be determined from the full quantum description.

quant-ph↗

arXiv2007

Ontological models and the interpretation of contextuality

Studying the extent to which realism is compatible with quantum mechanics teaches us something about the quantum mechanical universe, regardless of the validity of such realistic assumptions. It has also recently been appreciated that these kinds of studies are fruitful for questions relating to quantum information and computation. Motivated by this, we extend the ontological model formalism for realistic theories to describe a set of theories emphasizing the role of measurement and preparation devices by introducing `hidden variables' to describe them. We illustrate both the ontological model formalism and our generalization of it through a series of example models taken from the literature. Our extension of the formalism allows us to quantitatively analyze the meaning contextuality (a constraint on successful realistic theories), finding that - taken at face-value - it can be realized as a natural interaction between the configurations of a system and measurement device. However, we also describe a property that we call deficiency, which follows from contextuality, but does not admit such a natural interpretation. Loosely speaking, deficiency breaks a symmetry between preparations and measurements in quantum mechanics. It is the property that the set of ontic states which a system prepared in quantum state psi may actually be in, is strictly smaller than the set of ontic states which would reveal the measurement outcome psi with certainty.

quant-ph↗

arXiv2007

Loss Tolerant Linear Optical Quantum Memory By Measurement Based Quantum Computing

We give a scheme for loss tolerantly building a linear optical quantum memory which itself is tolerant to qubit loss. We use the encoding recently introduced in [Phys. Rev. Lett. 97, 120501, (2006)] and give a method for efficiently achieving this. The entire approach resides within the "One-way" model for quantum computing. Our results suggest that it is possible to build a loss tolerant quantum memory, such that if the requirement is to keep the data stored over arbitrarily long times then this is possible with only polynomially increasing resources and logarithmically increasing individual photon life times.

quant-ph↗

arXiv2007

Reference frames, superselection rules, and quantum information

Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etcetera. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This article reviews the role of reference frames and superselection rules in the theory of quantum information processing.

quant-ph↗

arXiv2007

Loss tolerance in one-way quantum computation via counterfactual error correction

We introduce a scheme for fault tolerantly dealing with losses (or other "leakage" errors) in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively using an adaptive strategy of measurement - no coherent measurements or coherent correction is required. Since the scheme relies on inferring information about what would have been the outcome of a measurement had one been able to carry it out, we call this "counterfactual" error correction.

quant-ph↗

arXiv2006

How to observe a coherent superposition of an atom and a molecule

We demonstrate that it is possible, in principle, to perform a Ramsey-type interference experiment to exhibit a coherent superposition of a single atom and a diatomic molecule. This gedanken experiment, based on the techniques of Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the commonly-accepted superselection rule that forbids coherent superpositions of eigenstates of differing atom number. This interference experiment makes use of a Bose-Einstein condensate as a reference frame with which to perform the coherent operations analogous to Ramsey pulses. We also investigate an analogous gedanken experiment to exhibit a coherent superposition of a single boson and a fermion, violating the commonly-accepted superselection rule forbidding coherent superpositions of states of differing particle statistics; in this case, the reference frame is realized by a multi-mode state of many fermions. This latter case reproduces all of the relevant features of Ramsey interferometry, including Ramsey fringes over many repetitions of the experiment. However, the apparent inability of this proposed experiment to produce well-defined relative phases between two distinct systems each described by a coherent superposition of a boson and a fermion demonstrates that there are additional, outstanding requirements to fully ``lift'' the univalence superselection rule.

quant-ph↗

arXiv2006

A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation

We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.

quant-ph↗

arXiv2006

Demonstration of efficient scheme for generation of "Event Ready" entangled photon pairs from single photon source

We present a feasible and efficient scheme, and its proof-of-principle demonstration, of creating entangled photon pairs in an event-ready way using only simple linear optical elements and single photons. The quality of entangled photon pair produced in our experiment is confirmed by a strict violation of Bell's inequality. This scheme and the associated experimental techniques present an important step toward linear optics quantum computation.

quant-ph↗

arXiv2006

Ontological Models for Quantum Mechanics and the Kochen-Specker theorem

Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are examined. The models are generalizations of Kochen and Specker's such model for a single 2-dimensional system - in particular a model for a three dimensional quantum system is considered in detail. Unfortunately, it appears the models do not quite reproduce the quantum mechanical statistics. They do, however, come close to doing so, and in as much as they simply involve probability distributions over the complex projective space they do reproduce pretty much everything else in quantum mechanics. The Kochen-Specker theorem is examined in the light of these models, and the rather mild nature of the manifested contextuality is discussed.

quant-ph↗

arXiv2006

Degradation of a quantum reference frame

We investigate the degradation of reference frames, treated as dynamical quantum systems, and quantify their longevity as a resource for performing tasks in quantum information processing. We adopt an operational measure of a reference frame's longevity, namely, the number of measurements that can be made against it with a certain error tolerance. We investigate two distinct types of reference frame: a reference direction, realized by a spin-j system, and a phase reference, realized by an oscillator mode with bounded energy. For both cases, we show that our measure of longevity increases quadratically with the size of the reference system and is therefore non-additive. For instance, the number of measurements that a directional reference frame consisting of N parallel spins can be put to use scales as N^2. Our results quantify the extent to which microscopic or mesoscopic reference frames may be used for repeated, high-precision measurements, without needing to be reset - a question that is important for some implementations of quantum computing. We illustrate our results using the proposed single-spin measurement scheme of magnetic resonance force microscopy.

quant-ph↗

arXiv2006

Measurement Induced Localization of Relative Degrees of Freedom

We present a comprehensive study, using both analytical and numerical methods, of measurement-induced localization of relational degrees of freedom. Looking first at the interference of two optical modes, we find that the localization of the relative phase can be as good for mixed states - in particular for two initially Poissonian or thermal states - as for the well-known case of two Fock states. In a realistic setup the localization for mixed states is robust and experimentally accessible, and we discuss applications to superselection rules. For an ideal setup and initial Fock states we show how a relational Schrödinger cat state emerges, and investigate circumstances under which such a state is destroyed. In our second example we consider the localization of relative atomic phase between two Bose Einstein condensates, looking particularly at the build up of spatial interference patterns, an area which has attracted much attention since the work of Javanainen and Yoo. We show that the relative phase localizes much faster than was intimated in previous studies focusing on the emerging interference pattern itself. Finally, we explore the localization of relative spatial parameters discussed in recent work by Rau, Dunningham and Burnett. We retain their models of indistinguishable scattering but make different assumptions. In particular we consider the case of a real distant observer monitoring light scattering off two particles, who records events only from a narrow field of view. The localization is only partial regardless of the number of observations. This paper contributes to the wider debate on relationism in quantum mechanics, which treats fundamental concepts - reference frames and conservation laws - from a fully quantum and operational perspective.

quant-ph↗

arXiv2005

Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist

A controversy that has arisen many times over in disparate contexts is whether quantum coherences between eigenstates of certain quantities are fact or fiction. We present a pedagogical introduction to the debate in the form of a hypothetical dialogue between proponents from each of the two camps: a factist and a fictionist. A resolution of the debate can be achieved, we argue, by recognizing that quantum states do not only contain information about the intrinsic properties of a system but about its extrinsic properties as well, that is, about its relation to other systems external to it. Specifically, the coherent quantum state of the factist is the appropriate description of the relation of the system to one reference frame, while the incoherent quantum state of the fictionist is the appropriate description of the relation of the system to another, uncorrelated, reference frame. The two views, we conclude, are alternative but equally valid paradigms of description.

quant-ph↗

arXiv2005

Entanglement-assisted Orientation in Space

We demonstrate that quantum entanglement can help separated individuals in making decisions if their goal is to find each other in the absence of any communication between them. We derive a Bell-like inequality that the efficiency of every classical solution for our problem has to obey, and demonstrate its violation by the quantum efficiency. This proves that no classical strategy can be more efficient than the quantum one.

quant-ph↗

arXiv2005

Symmetric Squares of Graphs

We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in an appendix.

math.CO↗

arXiv2005

A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effect it is only ever sensitive to the relational properties of the qubits.

quant-ph↗

arXiv2005

Resource-efficient linear optical quantum computation

We introduce a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons. We achieve a much greater degree of efficiency and a simpler implementation than previous proposals. We follow the "cluster state" measurement based quantum computational approach, and show how cluster states may be efficiently generated from pairs of maximally polarization entangled photons using linear optical elements. We demonstrate the universality and usefulness of generic parity measurements, as well as introducing the use of redundant encoding of qubits to enable utilization of destructive measurements - both features of use in a more general context.

quant-ph↗

arXiv2004

Decoherence-full subsystems and the cryptographic power of a private shared reference frame

We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a novel type of private shared correlation (distinct from private classical keys or shared entanglement) useful for cryptography. We present optimally efficient schemes for private quantum and classical communication given a finite number of qubits transmitted over an insecure channel and given a private shared Cartesian frame and/or a private shared reference ordering of the qubits. We show that in this context, it is useful to introduce the concept of a decoherence-full subsystem, wherein every state is mapped to the completely mixed state under the action of the decoherence.

quant-ph↗