Quantum Physics

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. This process can be used for irreversibly loading and cooling atoms within the lowest Bloch band of the lattice. I will describe loading and cooling schemes based on this mechanism and compare them to conventional loading schemes. I will then show how coherent dynamics in a very strongly interacting 1D optical lattice setup can be used for the efficient generation of arbitrary graph states in the atomic quantum register. This system can be mapped onto an XY spin chain which itself is equivalent to a system of non-interacting fermions. By exploiting the anticommutation relations between these fictitious fermions I will discuss how any graph state can be realized in an efficient and robust way. In the final part of my talk I will present a practical method for detecting and characterizing multipartite entangled states in atomic quantum registers. This scheme is based on measuring violations of entropic inequalities using simple quantum networks involving only two copies of the quantum state under consideration. I will investigate the performance of this method under realistic conditions taking into account the most common sources of experimental errors.

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 result is a theory of hidden variables, although it is not a hidden variable model of quantum theory because it is both local and noncontextual. Despite admitting a simple classical interpretation, the theory also exhibits the operational features of Bohr's notion of complementarity. In fact, it includes all of the features of quantum mechanics to which Bohr appeals in his response to EPR. This theory demonstrates, therefore, that Bohr's arguments fail as a defense of the completeness of quantum mechanics. Joint work with Stephen Bartlett and Terry Rudolph

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.

Collapse models are one of the most promising attempts to overcome the measurement problem of quanum mechanics: they descibe, within one single framework, both the quantum properties of microscopic systems and the classical properties of macroscopic objects, and in particular they explain why measurements always have definite outcomes, distributed according to the Born probability rule. We will discuss some recent developments in this field: i) we will show how it is possible to formulate collapse models in such a way that the mean energy of physical system does non increse indefinitely, a typical feature of the models first proposed in the literature; ii) we will discuss recent experiments aiming at testing the validity of the superposition principle, thus of collapse models, at the mesoscopic level.

We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches.

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.

I look at the information-processing involved in a quantum computation, in terms of the difference between the Boolean logic underlying a classical computation and the non-Boolean logic represented by the projective geometry of Hilbert space, in which the subspace structure of Hilbert space replaces the set-theoretic structure of classical logic. I show that the original Deutsch XOR algorithm, Simon's algorithm, and Shor's algorithm all involve a similar geometric formulation. In terms of this picture, I consider the question of where the speedup relative to classical algorithms comes from.

It is shown that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with non-standard field fluctuations (“quantum non-equilibrium”). It is shown that such non-equilibrium vacua lead to statistical anomalies, such as a breaking of scale invariance for the primordial power spectrum. The results depend only weakly on the details of the de Broglie-Bohm dynamics. Recent observations of the cosmic microwave background are used to set limits on violations of quantum theory in the early universe.

The problem of associating beables (hidden variables) to QFT, in the spirit of what Bohm did for nonrelativistic QM, is not trivial. In 1984, John Bell suggested a way of solving the problem, according to which the beables are the positions of fermions, in a discretized version of QFT, and obey a stochastic evolution that simulates all predictions of QFT. In the continuum limit, it will be shown that the Bell model becomes deterministic and that it is related to the choice of the charge density as a beable. Moreover, the charge superselection rule is a consequence of the Bell model. The non-relativistic limit and the derivation of Bohm's first quantized interpretation in this limit are also studied. I will also consider whether the Bell model can be applied to bosons.