Location of Repository

Quantum information theory promises many advances in science and technology. This thesis presents three different results in quantum information theory.\ud \ud The first result addresses the theoretical foundations of quantum metrology. It is now well known that quantum-enhanced metrology promises improved sensitivity in parameter estimation over classical measurement procedures. The Heisenberg limit is considered to be the ultimate limit in quantum metrology imposed by the laws of quantum mechanics. It sets a lower bound on how precisely a physical quantity can be measured given a certain amount of resources in any possible measurement. Recently, however, several measurement procedures have been proposed in which the Heisenberg limit seemed to be surpassed. This led to an extensive debate over the question how the sensitivity scales with the physical resources such as the average photon number and the computational resources such as the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a novel and ultimate Heisenberg limit that applies to all conceivable measurement procedures. Our approach to quantum metrology not only resolves the mentioned paradoxical situations, but also strengths the connection between physics and computer science.\ud \ud A clear connection between physics and computer science is also present in other results. The second result reveals a close relationship between quantum metrology and the Deutsch-Jozsa algorithm over continuous-variable quantum systems. The Deutsch-Jozsa algorithm, being one of the first quantum algorithms, embodies the remarkable computational capabilities offered by quantum information processing. Here, we develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter estimation protocol or the Deutsch-Jozsa algorithm. The procedure estimates a value of an unknown parameter with Heisenberg-limited precision or solves the Deutsch-Jozsa problem in a single run without the use of any entanglement.\ud \ud The third result illustrates how physical principles that govern interaction of light and matter can be efficiently employed to create a computational resource for a (one-way) quantum computer. More specifically, we demonstrate theoretically a scheme based on atomic ensembles and the dipole blockade mechanism for generation of the so-called cluster states in a single step. The entangling protocol requires nearly identical single-photon sources, one ultra-cold ensemble per physical qubit, and regular photo detectors. This procedure is significantly more efficient than any known robust probabilistic entangling operation

Publisher: Physics and Astronomy (Sheffield)

Year: 2011

OAI identifier:
oai:etheses.whiterose.ac.uk:1249

Provided by:
White Rose E-theses Online

Downloaded from
http://etheses.whiterose.ac.uk/1249/3/Zwierz%2C_Marcin.pdf

- (2006). A fault-tolerant one-way quantum computer.
- (2006). A high-brightness source of narrowband, identical-photon pairs.
- (2001). A scheme for eﬃcient quantum computation with linear optics.
- (1998). A silicon-based nuclear spin quantum computer.
- (2009). All-optical switching using the quantum Zeno eﬀect and two-photon absorption.
- (2008). Analysis of enhanced twophoton absorption in tapered optical ﬁbers.
- Applications of coherent population transfer to quantum information processing. Topic Review
- (2003). Atomic memory for correlated photon states.
- (2002). Atomic-vapor-based high eﬃciency optical detectors with photon number resolution.
- Atoms, dipole waves, and strongly focused light beams.
- (2008). Bell inequality violation with two remote atomic qubits.
- (2005). Breaking the Heisenberg limit with ineﬃcient detectors.
- Brokered graph-state quantum computation.
- (1936). Capture of slow neutrons.
- (2007). Cluster state preparation using gates operating at arbitrary success probabilities.
- (2006). Coherent excitation of Rydberg atoms in an ultracold gas.
- Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency.
- (1997). Coherent population trapping in laser spectroscopy.
- (2003). Coherent quantum dynamics of a superconducting ﬂux qubit.
- (1998). Cold bosonic atoms in optical lattices.
- (2007). Collisional decoherence during writing and reading quantum states.
- Colloquium: Trapping and manipulating photon states in atomic ensembles.
- (2005). Comment on ”Eﬃcient high-ﬁdelity quantum computation using matter qubits and linear optics”.
- (2007). Communication links for distributed quantum computation.
- (2008). Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms.
- (1999). Continuous variable quantum cryptography.
- (2005). Control of decoherence in the generation of photon pairs from atomic ensembles.
- (1999). Coupled quantum dots as quantum gates.
- (2002). Creating single-atom and single-photon sources from entangled atomic ensembles.
- (2000). Criteria for continuousvariable quantum teleportation.
- (2000). Dark-state polaritons in electromagnetically induced transparency.
- (2007). Design of a mode converter for eﬃcient light-atom coupling in free space.
- (2003). Deutsch-Jozsa algorithm for continuous variables.
- (2001). Dipole blockade and quantum information processing in mesoscopic atomic ensembles.
- (1992). Dispersive properties of electromagnetically induced transparency.
- (2007). Distributed measurement-based quantum computation.
- (1999). Distributed quantum computation over noisy channels.
- (2008). Distributed quantum computing: A new frontier in distributed systems or science ﬁction?
- (2003). Distributed quantum computing.
- (2008). Dynamics of low-density ultracold Rydberg gases.
- (2005). Eﬃcient high-ﬁdelity quantum computation using matter qubits and linear optics.
- (2005). Electromagnetically induced transparency with tunable singlephoton pulses.
- (2005). Electromagnetically induced transparency: Optics in coherent media.
- (1997). Electromagnetically induced transparency.
- (2010). Entanglement is not a critical resource for quantum metrology.
- (2000). Entanglement of atomic ensembles by trapping correlated photon states.
- (1999). Entanglement of atoms via cold controlled collisions.
- (1998). Entanglement of formation of an arbitrary state of two qubits.
- (2007). Entanglement of single-atom quantum bits at a distance.
- (2005). Entangling single- and N -atom qubits for fast quantum state detection and transmission.
- (1998). Error correction for continuous quantum variables.
- (2008). Experimental demonstration of a BDCZ quantum repeater node.
- (1998). Experimental implementation of fast quantum searching.
- (2007). Experimental procedures for entanglement veriﬁcation.
- (1998). Experimental realization of a quantum algorithm.
- (2001). Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance.
- (2008). Exponentially enhanced quantum metrology.
- (2000). Fast quantum gates for neutral atoms.
- (2003). Fault-tolerant quantum computation by anyons.
- (1996). Fault-tolerant quantum computation. In
- (2009). Full quantum analysis of two-photon absorption using two-photon wavefunction: Comparison with one-photon absorption.
- (2007). Functional quantum nodes for entanglement distribution over scalable quantum networks.
- (2010). General Cram´ er-Rao bound for parameter estimation using Gaussian multimode quantum resources.
- (2010). General optimality of the Heisenberg limit for quantum metrology.
- Generalized limits for single-parameter quantum estimation.
- (1996). Generalized uncertainty relations: Theory, examples, and Lorentz invariance.
- (2008). Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories.
- Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles.
- (1990). Geometry of quantum evolution.
- (2002). glu. High eﬃciency photon counting using stored light.
- (2007). Heralded entanglement between atomic ensembles: Preparation, decoherence, and scaling.
- (2008). High coherence photon pair source for quantum communication.
- (2007). High purity bright single photon source.
- (2009). High-eﬃciency cluster-state generation with atomic ensembles via the dipole-blockade mechanism.
- (2008). How much of one-way computation is just thermodynamics?
- (1990). Imamo˘ glu. Nonlinear optical processes using electromagnetically induced transparency.
- (2009). Interfacing light and single atoms with a lens.
- (1993). Interferometric detection of optical phase shifts at the Heisenberg limit.
- (2010). Introduction to Optical Quantum Information Processing.
- (2005). Introductory Quantum Optics.
- (2010). Lecture notes on optical quantum computing.
- (1999). Light speed reduction to 17 metres per second in an ultracold atomic gas.
- (2009). Limitations on continuous variable quantum algorithms with Fourier transforms.
- (2007). Linear optical quantum computing with photonic qubits.
- (2001). Long-distance quantum communication with atomic ensembles and linear optics.
- (2005). Long-range interactions and entanglement of slow single-photon pulses.
- (2008). Mapping photonic entanglement into and out of a quantum memory.
- (1987). Measurement of subpicosecond time intervals between two photons by interference.
- (2003). Measurement-based quantum computation on cluster states.
- (2009). Measurement-based quantum computation.
- (2005). Measurement-induced entanglement for excitation stored in remote atomic ensembles.
- (1997). Measuring the Quantum State of Light.
- (2008). Memory-built-in quantum teleportation with photonic and atomic qubits.
- (2003). Millimeter-wave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap: Quantum defects of the ns, np, and nd series.
- (1967). Minimum mean-squared error of estimates in quantum statistics.
- (2003). Multiparticle entanglement puriﬁ-cation for graph states.
- (2005). Multiparticle entanglement puriﬁ-cation for two-colorable graph states.
- (2004). Multiparty entanglement in graph states.
- (2009). Multipath entanglement of two photons.
- (2001). Observation of coherent optical information storage in an atomic medium using halted light pulses.
- (1991). Observation of electromagnetically induced transparency.
- (1987). Observation of nonclassical eﬀects in the interference of two photons.
- (2001). Observation of ultraslow and stored light pulses in a solid.
- (1943). On a measure of divergence between two statistical populations deﬁned by probability distributions.
- (2004). Optical quantum computation using cluster states.
- (2007). Optimal control of light pulse storage and retrieval.
- (1995). Optimal extraction of information from ﬁnite quantum ensembles.
- Optimal local implementation of nonlocal quantum gates.
- (2009). Optimizing type-I polarizationentangled photons.
- (2001). Persistent entanglement in arrays of interacting particles.
- (2005). Polarizationmomentum hyperentangled states: Realization and characterization.
- (2009). Private communication.
- (1998). Quantum algorithms revisited.
- (2010). Quantum analogue computing.
- (2000). Quantum Computation and Quantum Information.
- (1998). Quantum computation in quantum-Hall systems.
- (1999). Quantum computation over continuous variables.
- (1998). Quantum computation with quantum dots.
- (2007). Quantum computing with collective ensembles of multilevel systems.
- (2000). Quantum cryptography with squeezed states.
- (1969). Quantum detection and estimation theory.
- (2009). Quantum entanglement.
- (1998). Quantum error correction for communication with linear optics.
- (1999). Quantum information processing using quantum dot spins and cavity QED.
- (2008). Quantum information processing with single photons and atomic ensembles in microwave coplanar waveguide resonators.
- (2005). Quantum information with continuous variables.
- (2010). Quantum information with Rydberg atoms.
- (2010). Quantum interface between light and atomic ensembles.
- (1999). Quantum logic gates in optical lattices.
- (2002). Quantum memory for photons: Dark-state polaritons.
- (2006). Quantum metrology.
- (2010). Quantum Noise.
- (1997). Quantum telecomputation. e-print arXiv:quant-ph/9704012,
- (1981). Quantum-mechanical noise in an interferometer.
- (2001). Quantum-state engineering with Josephson-junction devices.
- (2008). Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions.
- (2002). Rabi oscillations in a large Josephson-junction qubit.
- (1992). Rapid solution of problems by quantum computation.
- (2009). Realization of coherent optically dense media via buﬀer-gas cooling.
- (2005). Repeat-until-success linear optics distributed quantum computing.
- (2006). Repeat-untilsuccess quantum computing using stationary and ﬂying qubits.
- (1987). Resonant-collision spectroscopy of Rydberg atoms.
- (1994). Rydberg Atoms.
- (2010). Scalable quantum computing with atomic ensembles.
- (2001). Secure quantum key distribution using squeezed states.
- (2004). Single-photon generation from stored excitation in an atomic ensemble.
- (2004). Single-shot read-out of an individual electron spin in a quantum dot.
- Spatial two-photon interference in a Hong-Ou-Mandel interferometer.
- (2008). Spatially resolved observation of dipole-dipole interaction between Rydberg atoms.
- (1981). Statistical distance and Hilbert space.
- Statistical distance and the geometry of quantum states.
- (2005). Storage and retrieval of single photons transmitted between remote quantum memories.
- (2001). Storage of light in atomic vapor.
- (2008). Strong interaction between light and a single trapped atom without the need for a cavity.
- (2004). Superconducting qubits: A short review.
- (2004). Suppression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms.
- (1998). Teleportation of continuous quantum variables.
- (2001). The focus of light - theoretical calculation and experimental tomographic reconstruction.
- (1954). The Quantum Theory of Radiation.
- (1993). The rate of evolution of a quantum state.
- (1945). The uncertainty relation between energy and time in non-relativistic quantum mechanics.
- (2009). Thresholds for topological codes in the presence of loss.
- (2007). Topological fault-tolerance in cluster state quantum computation.
- (2007). Topological stability of stored optical vortices.
- (2002). Two-photon linewidth of light ”stopping” via electromagnetically induced transparency.
- Ultrabright source of polarization-entangled photons.
- (2008). Ultrasensitive hot-electron nanobolometers for terahertz astrophysics.
- (2009). umel. Foundations of Quantum Mechanics: from Photons to Quantum Computers. Jones and Bartlett
- (1998). Unconditional Quantum Teleportation.
- (1990). Very cold trapped atoms in a vapor cell.
- (2005). Zeros of Rydberg-Rydberg F¨ oster interactions.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.