This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
Asymptotic statements like the almost-equi-partition law, the theorm of Shannon Mc -Millan-Breiman, the theorem of Sanov have all natural quantum analogs. They all talk about the thermodynamik limit of quantum spin systems. I will try to summarize these results and sketch the main ideas of proof.
The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this talk I shall relate the information spectrum approach to Shannon information theory and explore its relationship to ``entropic'' properties including subadditivity, chain rules, Araki-Lieb inequlities, and monotonicity.
We consider the problem of bounded-error quantum state identification: given one of two known states, what is the optimal probability with which we can identify the given state, subject to our guess being correct with high probability (but we are permitted to output "don't know" instead of a guess). We prove a direct product theorem for this problem. Our proof is based on semidefinite programming duality and the technique may be of wider interest. Using this result, we present two new exponential separations in the simultaneous message passing model of communication complexity.
A swashbuckling tale of greed, deception, and quantum data hiding on the high seas. When we hide or encrypt information, it's probably because that information is valuable. I present a novel approach to quantum data hiding based this assumption. An entangled treasure map marks the spot where a hoard of doubloons is buried, but the sailors sharing this map want all the treasure for themselves! How should they study their map using LOCC? This simple scenario yields a surprisingly rich and counterintuitive game theoretic structure.
will discuss how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control are brought together.
Bohrs Principle of Complementarity of wave and particle aspects of quantum systems has been a cornerstone of quantum mechanics since its inception. Einstein, Schrödinger and deBroglie vehemently disagreed with Bohr for decades, but were unable to point out the error in Bohrs arguments. I will report three recent experiments in which Complementarity fails, and argue that the results call for an upgrade of the Quantum Measurement theory. Finally, I will introduce the novel concept of Contextual Null Measurement (CNM) and discuss some of its surprising applications.
Optical experiments led the way to quantum information with striking examples of Bell's inequality tests and entangled state synthesis. Early demonstrations of quantum communication proved that optics are important for quantum communication and more recent ideas about linear optic quantum computing raised hopes that this would also be true for computing. I will give an overview of the various elements that are required for optical QIP and the state-of-the-art characteristics.
I shall discuss entanglement - assisted invariance (symmetry exhibited by correlated quantum states) and describe how it can be used to understand the nature of ignorance, and, hence, the origin of probabilities in quantum physics. WHZ, Phys. Rev. Lett. 90, 120404 (2003); Rev. Mod. Phys. 75, 715 (2003); Phys. Rev. 71, 052105 (2005) (quant-ph/0405161).