Quantum mechanics redefines information and its fundamental properties. Researchers at Perimeter Institute work to understand the properties of quantum information and study which information processing tasks are feasible, and which are infeasible or impossible. This includes research in quantum cryptography, which studies the trade-off between information extraction and disturbance, and its applications. It also includes research in quantum error correction, which involves the study of methods for protecting information against decoherence. Another important side of the field is studying the application of quantum information techniques and insights to other areas of physics, including quantum foundations and condensed matter.
Almost all known superpolynomial quantum speedups over classical algorithms have used the quantum Fourier transform (QFT). Most known applications of the QFT make use of the QFT over abelian groups, including Shor’s well known factoring algorithm [1]. However, the QFT can be generalised to act on non-abelian groups allowing different applications. For example, Kuperberg solves the dihedral hidden subgroup problem in subexponential time using the QFT on the dihedral group. The aim of this research is to construct an efficient QFT on SU(2). Most of the progress in constructing QFTs has come from applying ideas from classical algorithms such as subgroup adapted bases. For example, Moore et al. have applied classical ideas from e.g. to build non-abelian QFTs. Applying these ideas to infinite groups such as SU(2) requires new tools. The function must be sampled or discretised in a way so as to minimise the error. I will present some ideas based on classical algorithms which may lead to a QFT over the group SU(2) for band limited functions. There are problems with making these algorithms unitary that must be addressed and efficient methods for calculating coefficients (cf. the controlled phase gates in the abelian case) must be found.
An approximate quantum encryption scheme uses a private key to encrypt a quantum state while leaking only a very small (though non-zero) amount of information to the adversary. Previous work has shown that while we need 2n bits of key to encrypt n qubits exactly, we can get away with only n bits in the approximate case, provided that we know that the state to be encrypted is not entangled with something that the adversary already has in his possession. In this talk I will show a generalization of this result: approximate quantum encryption requires roughly n-t bits of key, where t is a lower bound on the conditional min-entropy of the state to be encrypted given the adversary's prior knowledge. Along the way, I will introduce a quantum version of entropic security and show how the approximate quantum encryption scheme fits within this framework. This is joint work with Simon-Pierre Desrosiers.
Imperfections in devices are inevitable in practice. In this talk, we focus on the imperfection of QKD systems in the detectors, namely that the efficiencies of the detectors are not completely identical. We show some practical attacks that specifically exploit this efficiency mismatch and demonstrate how Eve may obtain some information on the final key if Alice and Bob are unaware of the attack. Also, we discuss the upper and lower bounds on the secret key rates both with and without the assumption of the efficiency mismatch
I will introduce Kitaev's suface codes as a block quantum error-correcting code. Recovery procedures will be described in the case of imperfect syndrome measurements. More might be covered if time permits.
Imagine that Alice and Bob share a quantum state, from which they want to distill something useful like entanglement or secret key. For this they need to communicate classically and they want to do this by one way communication from Alice to Bob. For some states, it might happen that the state is a part of a tripartite state shared with Charlie, which is invariant if Bob's and Charlie's systems are switched. Such a state is called a symmetric extension, and if it exists Alice and Bob have no chance of distilling key or entanglement by one way communication. I will present some results characterizing which quantum states have symmetric extension.
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.