Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Quantum tomography and fidelity estimation of multi-partite systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this talk I could explain an efficient way (i.e., in polylog(d) time, with d the dimension of the Hilbert space) to perform tomography and estimate the fidelity of generalized coherent state (GCS) preparation. GCSs differ from the well known coherent states in that the associated Hilbert space is finite dimensional.
Projections onto mutually unbiased bases (MUBs) have the ability to maximize information extraction per measurement and to minimize redundancy. I present an experimental demonstration of quantum state tomography of two-qubit polarization states that takes advantage of MUBs. Estimates of the state taken with this method have a measurably higher fidelity to the true state than estimates taken using standard measurement strategies. I explain how this advantage can be understood from the structure of the measurements we use.
A number of problems in quantum estimation can be formulated as a convex optimization [1]. Applications include: maximum likelihood estimation, optimal experiment design, quantum state detection, and quantum metrology under instrumentation constraints. This talk will draw on the work I have been involved with, e.g., [2], [3], [4]. Our work in optimal quantum error correction [5, 6] is also relevant. Great benefit is derived using an error model which is specific to the system. Obtaining the errors from tomography is a logical route. How to do this, however, is an open question.
Theoretical and experimental results on the Quantum Injected Optical Parametric Amplification (QI-OPA) of optical qubits in the high gain regime (g > 6) are reported. The entanglement of the related Schroedinger Cat-State (SCS) is demonstrated as well as the establishment of Phase-Covariant quantum cloning for a Macrostate consisting of about 106 particles. In addition, the violation of the CHSH inequality is has been realized experimentally.
When one makes squeezed light by downconversion of a pulsed pump laser, many temporal / spectral modes are simultaneously squeezed by different amounts. There is no guarantee that any of these modes matches the pump or the local oscillator used to measure the squeezing in homodyne detection. Therefore the state observed in homodyne detection is not pure, and many photons are present in the beam path that do not lie in the local oscillator\'s mode. These problems limit the fidelity of quantum information processing tasks with pulsed squeezed light.
We propose and demonstrate experimentally a technique for estimating quantum-optical processes in the continuous-variable domain. The process data is determined by applying the process to a set of coherent states and measuring the output. The process output for an arbitrary input state can then be obtained from its Glauber-Sudarshan expansion. Although such expansion is generally singular, it can be arbitrarily well approximated with a regular function.
I will discuss our ongoing attempts to construct Symmetric Informationally Complete Positive Operator Valued Measures, or (minimal) two designs, out of Gaussian states. This poses difficulties both in principle, such as how to introduce a measure on the noncompact group of symplectic transformations, as well as in practice, such as how to truncate the space of states in an experimentally useful way. Joint work with Robin Blume-Kohout.
I\'ll survey recent results from quantum computing theory showing that,if one just wishes to learn enough about a quantum state to predictthe outcomes of most measurements that will actually be made, then itoften suffices to perform exponentially fewer measurements than wouldbe needed in quantum state tomography. I\'ll then describe the resultsof a numerical simulation of the new quantum state learning approach.The latter is joint work with Eyal Dechter.
We introduce the concept of tight POVMs. In analogy with tight frames, these are POVMs that are as close as possible to orthonormal bases for the space they span. We show that tight rank-one POVMs define the exact class of optimal measurements for linear tomography of quantum states. In this setting they are equivalent to complex projective 2-designs. We also show that tight POVMs define the optimal class of measurements on the probe state for ancilla-assisted process tomography of unital channels. In this setting they are equivalent to unitary 2-designs.