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.
In quantum information, one can prove that a secure quantum cryptography channel based on photon key distribution requires reliable single photon sources. If not, a potential eavesdropper may be able to get information using the extra photons. Current sources are based on either attenuated laser beams, which may produce randomly 2 or even more photons at a time following a poissonian statistics, or either based on two level-systems providing single photon sources often requiring cooling or complex set-ups.The goal of our experiment is to provide an easy, robust and compact single photon source using nonlinear optics (parametric down-conversion). We want to study its statistics and compare it to other photon sources. We could use this heralded single photon source to create a quantum communication channel.
I will present an efficient quantum algorithm for an additive
approximation of the famous Tutte polynomial of any planar graph at
any point. The Tutte polynomial captures an extremely wide range of
interesting combinatorial properties of graphs, including the
partition function of the q-state Potts model. This provides a new
class of quantum complete problems.
Our methods generalize the recent AJL algorithm for the approximation
of the Jones polynomial; instead of using unitary representations, we
allow non-unitarity, which seems counter intuitive in the quantum
world. Significant contribution of this is a proof that non-unitary
operators can be used for universal quantum computation.
In nearly every quantum algorithm which exponentially outperforms the best classical algorithm the quantum Fourier transform plays a central role. Recently, however, cracks in the quantum Fourier transform paradigm have begun to emerge. In this talk I will discuss one such development which arises in a new efficient quantum algorithm for the Heisenberg hidden subgroup problem. In particular I will show how considerations of symmetry for this hidden subgroup problem lead naturally to a different transform than the quantum Fourier transform, the Clebsch-Gordan transform over the Heisenberg group. Clebsch-Gordan transforms over finite groups thus appear to be an important new tool for those attempting to find new quantum algorithms. [Part of this work was done in collaboration with Andrew Childs (Caltech) and Wim van Dam (UCSB)]
I will survey recent feasibility results on building multi-party cryptographic protocols which manipulate quantum data or are secure against quantum adversaries. The focus will be protocols for secure evaluation of quantum circuits. Along the way, I'll discuss how quantum machines can (and can't) prove knowledge of a secret to a distrustful partner. The talk is based on recent unpublished results, as well as older joint work with subsets of Michael Ben-Or, Claude Crepeau, Daniel Gottesman, and Avinatan Hasidim (STOC '02, FOCS '02, Eurocrypt '05, FOCS '06).
Inelastic collisions occur in Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, these processes have not been studied in the case when particles do not escape the trap. We show that such inelastic processes are relevant in quantum properties of the system such as the evolution of the relative population and entanglement. Moreover, including inelastic terms in the models of multimode condensates allows for an exact analytical solution.
After a brief overview of the three broad classes of superconducting quantum bits (qubits)--flux, charge and phase--I describe experiments on single and coupled flux qubits. The quantum state of a flux qubit is measured with a Superconducting QUantum Interference Device (SQUID). Single flux qubits exhibit the properties of a spin-1/2 system, including superposition of quantum states, Rabi oscillations and spin echoes. Two qubits, coupled by their mutual inductance and by screening currents in the readout SQUID, produce a ground state |0> and three excited states |1>, |2> and |3>. Microwave spectra reveal an anticrossing between the |1>and |2> energy levels. The level repulsion can be reduced to zero by means of a current pulse in the SQUID that changes its dynamic inductance and hence the coupling between the qubits. The results are in good agreement with predictions. The ability to switch the coupling between qubits on and off permits efficient realization of universal quantum logic. This work was in collaboration with T. Hime, B.L.T. Plourde, P.A. Reichardt, T.L. Robertson, A. Ustinov, K.B. Whaley, F.K. Wilhelm and C.-E. Wu, and supported by AFOSR, ARO and NSF.
Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is
excluded.) In this talk I show how states that minimize uncertainty in this sense can be generated via a discrete phase space based on finite fields. I also discuss some numerically observed features of these minimum-uncertainty states as the dimension d gets very large.
Thermodynamics places surprisingly few fundamental constraints on
information processing. In fact, most people would argue that it imposes
only one, known as Landauer's Principle: a process erasing one bit of
information must release an amount kT ln 2 of heat. It is this simple
observation that finally led to the exorcism of Maxwell's Demon from
statistical mechanics, more than a century after he first appeared.
Ignoring the lesson implicit in this early advance, however, quantum
information theorists have been surprisingly slow to embrace erasure as a
fundamental primitive. Over the past couple of years, however, it has
become clear that a detailed understanding of how difficult it is to erase
correlations leads to a nearly complete synthesis and simplification of
the known results of asymptotic quantum information theory. As it turns
out, surprisingly many of the tasks of interest, from distilling
high-quality entanglement to sending quantum data through a noisy medium
to many receivers, can be understood as variants of erasure. I'll sketch
the main ideas behind these discoveries and end with some speculations on
what lessons the new picture might have for understanding information loss in real physical systems.
We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.
We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state. One implication of this is that the entanglement in these states is very robust (persistent), while an application is in establishing an arbitrary amount of entanglement between well-separated parties (for subsequent use as a communication
resource) by local measurements on an appropriate graph. Based on quant-ph/0602139.
We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. We discuss the question, how the theory of information processing looks like in the framework of the generalised quantum theory. In particular we propose a scheme of extended dense coding, in which one transmits two qubits by sending one extended bit, provided it was initially entangled with the extended bit of the receiver.