My life has been a blessing from God in many ways.First and foremost, I would like to thank professors Cass Sackett and Bill Soffa for encouraging and never giving up on me.The completion of my study could not have happened without them.In reaching the apex of my endeavor, I am forever indebted in gratefulness.Without their help, this would have been an impossible journey.They also inspired me to consider teaching as my new goal.Despite other lucrative offers, I believe teaching has a true meaning and purpose for me.I'd also like to thank graduate students in Casslab, especially Rob Horne, who shared the burden of making our experiment a successful one.My life re-started in the states at ten years old, when barely speaking a word of English, Bob Schmitt and Greg Bartman became my lifelong friends.Mr. & Mrs (Mom) Bartman never seemed to get tired of my coming over to their house/beach house living like a son who never paid rent.In Laurel high school, I would like to thank Mr. Swartz for making math an approachable subject.I must also thank Mr/Coach Chuck Hickes for believing in my success -not only were you my football coach, you coached me in so many other ways in life!At Swarthmore, Professor John Gaustad took me under his wings and taught me how to study and do research.You did everything you could to make sure I could be successful at research through experiments.My 6 years spent at NASA proved to be a very valuable experience in many ways.Ed Cheng, Dale Fixsen, and John Mather were three significant influences in my life.I still remember Casey Inman teaching me how to make circuits.I had an unforgettable experience at Antarctica, running the CMBR experiment.It's funny how one opportunity leads to another, who would have thought I'd meet my wife Yeonju (Sarah) there, and name our daughters Erebus and Terranova after the mountains in Antarctica.My 14 years at the Naval Research Lab are unforgettable ones.It took me everywhere including Afghanistan.My thanks go to Charmaine Gilbreath, who provided the opportunity for me to pursue graduate studies.Before coming to UVa, my short stint at GWU was not a waste.I'd like to thank professor Helmut Haberzettl for his German way of physics.I also like to
A formula for the commutator of tensor product matrices is used to show that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site, and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial'' n-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of paradoxes of the type of the Kochen-Specker theorem, which can then be easily rephrased into proposals for no-hidden-variable experiments of the type of the ``Bell theorem without inequalities.''