Traditionally, we use the quantum Fourier transform circuit (QFT) in order to perform quantum phase estimation, which has a number of useful applications. The QFT circuit for a binary field generally consists controlled-rotation gates which, when removed, yields the lower-depth approximate QFT circuit. It is known that a logarithmic-depth approximate QFT circuit is sufficient to perform phase estimation with a degree of accuracy negligibly lower than that of the full QFT. However, when the depth of the AQFT circuit becomes even lower, the phase estimation procedure no longer produces results that are immediately correlated to the desired phase. In this talk, I will explore the possibility of retrieving this information with classical analysis and with computer post-processing of the measured results of a low-depth AQFT circuit in a phase estimation algorithm.
"Most of the experimental advances in coherent quantum control in recent years have involved ultrashort pulses and pulse shaping techniques. These pulses have been an excellent source of coherent light with precise phase relationship between the various frequency components. In several recent works we have investigated the possibility of using broadband nonclassical light, generated by down-conversion of narrow-band lasers, for coherent control.We demonstrated that pulse shaping techniques can be used in the single-photon limit, when the light is composed of individual time-energy entangled photons. We could shape the two-photon correlation function, which is as close as one can get to ‘shaping of individual photons’. Using polarization pulse-shaping techniques we also controlled the quantum interference of polarization entangled photons. By controlling both phase and polarization of the photon-pairs, we were able to tailor the Hong-Ou-Mandel interference pattern, and generate all four polarization Bell-states.We believe that the combination of quantum control techniques with quantum optics could add an important ingredient to the toolbox of quantum information and computing."
Proving the additivity of the classical capacity of quantum channels is a major open problem in quantum information. This problem is related to the multiplicativity of certain norms with respect to the tensor product. These problems are introduced and some approached to resolving them are discussed. Several special cases that have been solved are also mentioned.
Any implementation of a quantum computer will require the ability to reset qubits to a pure input state, both to start the computation and more importantly to implement fault-tolerant operations. Even if we cannot reset to a perfectly pure state, heat-bath algorithmic cooling provides a method of purifying mixed states. By combining the ability to pump entropy out of the system through a controllable interaction with a heat bath and coherent control of the qubits, we are able to cool a subset of the qubits far below the heat bath temperature. Here we show an implementation of this cooling in a solid state NMR quantum information processor which offers high fidelity control of the qubit system and controllable access to a heat bath. We demonstrate an implementation of multiple rounds of heat-bath algorithmic cooling on three qubits and discuss the improvements in control techniques which have allowed us to show the purification of a single qubit to one and a half times the heat bath polarization.
In this study, we are interested in the practical question of how many times a quantum directional reference frame (i.e., a spin-J system) can be used to perform a certain task with a given probability of success, under the assumption that the quantum directional reference frame evolves under a map that is covariant under rotations in SU(2). Our main theorem restricts the form of the state of the quantum reference frame as a function of how many times the covariant map was applied to it. Our results are a generalization of the paper of Bartlett el al. on the degradation of reference frames, and can be used to analyze certain types of interactions on a spin-J system.
Current physical implementations of quantum key distribution (QKD) require communicating parties to be close together. We will explore methods for allowing parties separated by long distances to communicate by combining many QKD links in a network and discuss the resulting security properties.
Previous experiments on the production of entangled photon pairs directly in optical fiber via four-wave mixing (FWM) have used a single pump laser and produced signal and idler photons with similar wavelengths. We will present the first results of our investigation into the production of widely separated entangled photon pairs via FWM in optical fiber using multiple pump lasers also at widely separated wavelengths. This source will have important applications in quantum cryptography and computation. As fiber optic and free space quantum communication networks require photons at different wavelengths (1550 nm and around 800 respectively) this source will make hybrid quantum cryptography networks achievable and could also be used as a heralded optical fiber source of single photons.
"Distributed phase reference schemes are a new class of protocols for Quantum Key Distribution, in which the quantum signals have overall phase-relationships to each other. This is expected to protect against some loss-related attacks. However, proving the full security of these schemes is a new challenge for theorists, as one can no longer identify individual signals (such as qubits in BB84, for instance), and so the security proof techniques do not apply directly.In this talk I will present two such protocols (the Differential Phase Shift and the Coherent One Way protocols). Their ""unconditionnal security"" has not been proven yet, but I will present some specific attacks on these schemes, which give us upper bounds for the security, as well as a ""feeling"" on how these schemes should perform."
Many authors have proposed what are known as "phase-space" or "classical" representations of quantum mechanics. A unifying framework is given which illustrates the relationship among these various theories. Examples relevant to quantum computing will be given.