Quantum Physics

The mysteries of quantum theory run deep. Despite 80 years of research, there is still no consensus on its interpretation. This talk will explore some of the important issues in the foundations of quantum theory, from the idea that we have only a limited knowledge of a deeper reality, like the prisoner in Plato’s cave who sees only the shadows of objects and never the objects themselves, to John Bell’s famous discovery of the difference between quantum correlations and Dr. Bertlmann’s socks, namely, that whereas the mismatched colours of the doctor’s socks can be attributed to a decision at the sock drawer that morning, certain quantum correlations cannot be explained by a common cause, at least not without doing violence to some cherished principles of physics, such as the fact that causes cannot travel faster than the speed of light.

This panel will explore some of the deepest questions facing those who would harness the power of quantum mechanics in new quantum technologies: What are the newest and most interesting discoveries researchers have made about quantum information? What progress has been made in recent years towards experimentally harnessing quantum devices for quantum computation? What are the main motivations for building quantum information processing technologies? Drs. Aharonov and Shor appear courtesy of Institute for Quantum Computing.

Quantum computers hold the promise to revolutionize the way we secure information, compute and understand the quantum world. Although general-purpose quantum computers appear to be a long way off, we do have good test-beds of small quantum processors. One of the most versatile quantum test-beds is nuclear magnetic resonance (NMR): a version of which is familiar to many in the guise of the medical imaging modality, MRI. In fact NMR has broad importance to society: it is used in drug discovery, in oil exploration and to monitor the processing of cheese and chocolate. We will introduce NMR, show how it helps us understand quantum computing and we will look at how concepts based on quantum computing can improve NMR applications.

Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of the probability calculus and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that an agent’s degrees of belief be coherent. I argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. On this view, the familiar constraints of coherence only apply to sets of degrees of belief that could in principle be jointly verified. Accordingly, the constraints that coherence imposes on degrees of belief are generally weaker than the familiar ones. I then consider the implications of this interpretation of de Finetti for probabilities in quantum mechanics, focusing on the EPR/Bohm experiment and Bell’s theorem.

Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed hard instances where adiabatic optimization requires exponential time. In spite of this, there was still hope that this would not happen for random instances of NP-complete problems. This is an important issue since random instances are a good model for hard instances that can not be solved by current classical solvers, for which an efficient quantum algorithm would therefore be desirable. Here, we will show that because of a phenomenon similar to Anderson localization, an exponentially small eigenvalue gap appears in the spectrum of the adiabatic Hamiltonian for large random instances, very close to the end of the algorithm. This implies that unfortunately, adiabatic quantum optimization also fails for these instances by getting stuck in a local minimum, unless the computation is exponentially long. Joint work with Boris Altshuler and Hari Krovi

According to hidden-variables theories, quantum physics is a special 'equilibrium' case of a much wider 'nonequilibrium' physics. We describe the search for that wider physics in a cosmological context. The hypothesis that the universe began in a state of quantum nonequilibrium is shown to have observable consequences. In de Broglie-Bohm theory on expanding space, relaxation to quantum equilibrium is shown to be suppressed for field modes whose quantum time evolution satisfies a certain inequality, resulting in a 'freezing' of early nonequilibrium for these particular modes. For an early radiation-dominated expansion, the inequality implies a corresponding physical wavelength that is larger than the (instantaneous) Hubble radius. These results make it possible, for the first time, to make quantitative predictions for deviations from quantum theory. We consider, in particular, corrections to inflationary predictions for the cosmic microwave background, and the possibility of finding relic cosmological particles that violate the laws of quantum mechanics. (Reference: De Broglie-Bohm Prediction of Quantum Violations for Cosmological Super-Hubble Modes, http://arxiv.org/abs/0804.4656.)

Applications of quantum theory to cryptography and computation; understanding in more concrete, physical terms what quantum theory is telling us about the nature of reality. Applications of information theory to better understand the quantum “wave function”.

Applications of the quantum nature of our universe to potential new technologies like quantum cryptography and quantum computation. In particular, theoretical developments such as fault-tolerant quantum codes and protocols for quantum error correction.

Spacelike separated classical interventions make us to rethink what is quantum and what is classical. Quantum Lorentz transformations show that identification of subsystems is a tricky business, ditto entropy, entanglement and thermodynamic quantities. Resolution of information loss problem in black hole physics is tied to a construction of a theory of quantized gravity.

Abstract: Efforts to extrapolate non-relativistic (NR) quantum mechanics to a covariant framework encounter well-known problems, implying that an alternate view of quantum states might be more compatible with relativity. This talk will reverse the usual extrapolation, and examine the NR limit of a real, classical scalar field. A complex scalar \psi that obeys the Schrodinger equation naturally falls out of the analysis. One can also replace the usual operator-based measurement theory with classical measurement theory on the scalar field, and examine the NR limit of this as well. In this limit, the local energy density of the field scales as |\psi|^2, adding credibility to this approach. With the added postulate that "all measurements correspond to boundary conditions that extremize the classical action" (see arXiv:0906.5409), additional quantitative comparisons emerge between this \psi and the standard quantum wavefunction. Uncertainty can then be introduced (along with a "collapse" due to Bayesian updating) by simply giving the classical scalar field two components instead of one, leading to an intriguing \psi-epistemic model.