Talks

Arguably, the most important issue in physics today is trying to unify the twin pillars of modern physics, quantum theory and general relativity, into a single theory known as quantum gravity. This introductory presentation will discuss various aspects of quantum gravity.

I will review the published quasar absorption line constraints on variations in the fine-structure constant, alpha, focusing on the apparent disagreement between those derived from Keck/HIRES and VLT/UVES spectra which have provided evidence for and against alpha variation, respectively. I demonstrate simple yet fundamental flaws in the UVES constraints which preclude reliable comparison with those from HIRES. I will outline our program to obtain a definitive UVES measurement. I will also present several new absorption line constraints on variations in the proton-to-electron mass ratio, mu. For the two molecular hydrogen absorbers from which previous authors found tentative evidence for mu-variation, we find robustly null results. A further two molecular hydrogen absorbers, including an entirely new system, also yield tight, null constraints. Finally, I present new, detailed comparison of a radio absorption system containing ammonia inversion and molecular rotational transitions which yields the strongest current astrophysical constraint on mu-variation, dmu/mu=[mu(z)-mu(lab)]/mu(lab)=[+0.74+/-0.47(stat)+/-0.76(sys)]x10^-6, at redshift z=0.685.

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuits, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver\'s half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender\'s side. We discuss the advantages and disadvantages for each of the two codes.

We investigate the strengths and weaknesses of the Spekkens toy model for quantum states. We axiomatize the Spekkens toy model into a set of five axioms, regarding valid states, transformations, measurements and composition of systems. We present two relaxations of the Spekkens toy model, giving rise to two variant toy theories. By relaxing the axiom regarding valid transformations a group of toy operations is obtained that is equivalent to the projective extended Clifford Group for one and two qubits. However, the physical state of affairs resulting from this relaxation is undesirable, violating the desideratum that single toy bit operations must compose under the tensor product. The second variant toy theory is obtained by relaxing the axioms regarding valid states and measurements, resulting in a toy model that exhibits the Kochen-Specker property. Like the previous toy model, the relaxation renders the toy model physically undesirable. Therefore, we claim that the Spekkens toy model is optimal; altering its axioms does not yield a better epistemic description of quantum theory. This work is a collaboration with Gilad Gour, Aidan Roy and Barry C. Sanders.