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.
After working on this for the past week, I\'m pretty excited about his topic. The method allows easy visualization of single qubit rotations and separable projections, much like the Poincare sphere for one qubit states.
Let us assume a following scenario: In a state of a quantum system one qubit is encoded. The first observer has no prior knowledge about the state of the qubit. He performs an optimal measurement on the system and based on the measured data he estimates the state on the qubit. After performing the measurement the first observer leaves the measured quantum system in a lab. I will study the question whether the second observer who has no knowledge about the measurement setup and the measurement outcome of the first observation can learn anything about the original preparation of the qubit.
Assume one laboratory designed a technique to produce quantum states in a given state $ ho$. The other lab wants to generate exactly the same state and they produce states $sigma$. If we want to know how well the second lab is doing we need to characterize the distance between $sigma$ and $ ho$ by some means,e.g. by trying to measure their fidelity, which allows us to find the Bures distance between them. The task is simple if the given state is pure, $ ho=|psi angle langle psi|$, since then fidelity reduces to the expectation value, $F=langlepsi| sigma| psi angle$.
We study two related estimation problems involving phase- covariant quantum states. We first address the problem of phase estimation. We give optimal bounds for pure and mixed Gaussian states and find that for a fixed squeezing parameter a larger temperature can enhance the estimation fidelity. In addition we use state estimation concepts to give a benchmark that asses whether experimental implementations of quantum storage and teleportation protocols could be reproduced by classical means, i.e., by a measure and prepare strategy.
The field of linear optics quantum computing (LOQC) allows the construction of conditional gates using only linear optics and measurement. This quantum computing paradigm bypasses a seemingly serious problem in optical quantum computing: it appears to be very hard to produce a meaningful interaction between two single photons. But what if this obstacle were instead an advantage?
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.
Check back for details on the next lecture in Perimeter's Public Lectures Series