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.
Entanglement entropy is currently of interest in several areas in physics, such as condensed matter, field theory, and quantum information. One of the most interesting properties of the entanglement entropy is its scaling behavior, especially close to phase transitions. It was believed that for dimensions higher than 1 the entropy scales like surface area of the subsystem. We will describe a recent result for free fermions at zero temperature, where the entropy in fact scales faster. The latter problem will be related to a mathematical conjecture due to H. Widom (1982).
While modern theories lavishly invoke several spatial dimensions within models that seek to unify relativity theory and quantum mechanics, none seems to consider the possibility that a yet-unfamiliar aspect of time may do the work. I introduce the notion of Becoming and then consider its consequences for physical theory. Becoming portrays a possible aspect of time that is "curled" very much like the extra spatial dimensions in superstring theories.
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In addition to being a potentially useful tool in the study of standard oracles, Hamiltonian oracles naturally introduce the concept of fractional queries and are amenable to study using techniques of differential equations and geometry. As an example of these ideas we shall examine the Hamiltonian oracle corresponding to the problem of oracle interrogation. This talk is intended for all those who wish to apply their knowledge of differential geometry without the risk of creating an event horizon.
I will investigate the creation and detection of multipartite entangled states in systems of ultracold neutral atoms trapped in an optical lattice. These setups are scalable, highly versatile and controllable at the quantum level. Thus they provide an ideal test bed for studying the properties of multipartite entangled states. I will first present methods exploiting incoherent dynamics for initializing an atomic quantum register. The immersion of an optical lattice in a Bose-Einstein condensate leads to spontaneous emission of phonons.
I will discuss a toy theory that reproduces a wide variety of qualitative features of quantum theory for degrees of freedom that are continuous. The ontology of the theory is that of classical particle mechanics, but it is assumed that there is a constraint on the amount of knowledge that an observer may have about the motional state of any collection of particles -- Liouville mechanics with an epistemic restriction. The formalism of the theory is determined by examining the consequences of this "classical uncertainty principle" on state preparations, measurements, and dynamics.
The amount of nonlocality in the GHZ state can be quantified by determining how much classical communication is required to bring a local-hidden-variable model into agreement with the predictions of quantum mechanics. It turns out that one bit suffices, and, of course, nothing less will do. I will discuss generalizations of this result to graph states and its relation to the stabilizer formalism.
Quantum information methods have been recently used for studying the properties of ground state entanglement in several many body and field theory systems. We will discuss a thought experiment wherein entanglement can be extracted from the vacuum of a relativistic field theory into a pair of arbitrarily spatially separated atoms. In order to simulate the detection process, we will consider the ground state of a linear chain of cooled trapped ions, and discuss a scheme for detecting the entanglement between the ion's motional degrees of freedom.
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.