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Research Interests

At present, the field of Quantum Thermodynamics is an incredibly active one, and is where much of my focus lies. I'm also very interested in using insights from quantum informatin theory to probe quantum gravity. I am currently engaged in research projects in several fields. I am particularly interested in quantum information theory, quantum gravity, black hole thermodynamics, and the foundations of quantum theory. Although these fields are often distinct, there are many conceptual overlaps, as can be seen below.

Selected publications

Quantum information theory

"You don't understand quantum mechanics, you just get used to it."
-- attributed to Feynman, borrowed from von Neumann.

Quantum information theory is currently a very exciting field, and we are constantly learning new and surprising things about quantum mechanics. I am presently studying various topics mostly in quantum information theory, quantum cryptography, and entanglement manipulation.

Much of my work is in understanding the basic blocks of quantum information theory -- what does it mean for one quantum system to have information about another system. This is often best understood through communication theory. If an individual has a lot of information about my system, then I don't need to send them many qubits for them to possess the rest of my state. It was this idea which led to state merging and negative information.

Quantum gravity and black hole thermodynamics

"The hardest thing of all is to find a black cat in a dark room,
especiall if there is no cat."

My latest research has been in developing a consistent theory of quantum field theory coupled to classical gravity. Although there are a number of no go theorems which prevent this, they do not apply to post-quantum theories such as those which are fundamentally stochastic. These theories do not need the measurement postulate of quantum mechanics as they naturally lead to the collapse of the wave-function. See
A post-quantum theory of classical gravity

Many researchers believe that understanding black hole thermodynamics and the origin of black hole entropy is the key to understanding quantum gravity. At the moment, I'm interested in using tools from quantum information theory to understand problems such as black hole information loss, and information destruction. Some projects includes work with Bill Unruh on entangled black holes and the AMPS gedanken experiment (regarding firewalls), work on black holes and polyamory and a project with Benni Reznik showing that one can have information destruction, in a theory which is both local, and obeys conservation laws.

Also, information theory has forced us to re-examine many of the assumptions that were made in the early days of the black hole information paradox (such as the assumption that information is additive). For example, we have found that from the point of view of an experimenter, there can be situations where the black hole evaporation contains no information about the internal state of the black hole until the final burst of (low entropy) radiation unlocks all the information. This is in contrast to the usual assumptions that were made in the early days of attempts to understand the information loss puzzle, where locking information required an effective black-hole remnant with large entropy.

Quantum Thermodynamics

"In this house, young lady, we obey the laws of thermodynamics!"
--Homer Simpson

The laws of thermodynamics govern much of the world around us ??? they tell us that a hot cup of tea in a cold room will cool down rather than heat up; they tell us that unless we are vigilant, our houses will become untidy rather than spontaneously tidy; they tell us how efficient the best heat engines can be. But the laws of thermodynamics only apply to large objects, when many particles are involved. Can the laws of thermodynamics be applied to small systems, such as the kind of microscopic motors currently been fabricated in labs? Or perhaps even quantum systems? Surprisingly, the answer is yes. I'm interested in formulating laws of thermodynamics for quantum systems. We find for example, that at the small scale, there are
many second laws, not just one, and that we can formulate a stronger version of the zeroth law which helps us to naturally define the notion of temperature. This builds on some of my previous work deriving thermo-majorisation criteria, which was proven to be necessary and sufficient for thermodynamical state transformations.

I'm also interested in understanding systems which are smaller than the size of their interactions. Ordinarily, when one looks at the thermodynamical properties of a system, one assumes that interactions are either short range, or are screened. However, when interactions are taken into account, one finds that quantities which are usually extensive (such as the energy and entropy which scale as the size of the system), or intensive (such as the temperature and pressure, which are independent of the system's size), no longer remain so. Examples of such cases are gravitational systems (and in particular, black holes), and systems with entanglement entropy. Understanding non-extensive statistical mechanics and thermodynamics may be highly important in understanding black holes and systems where the entropy of entanglement play a role.

I have been developing new methods for studying the thermodynamics of systems with long-range interaction. I have been looking at various scaling relations which become important in non-extensive systems (for example, the Gibbs-Duhem relation no longer holds). For example, entropy becomes area scaling, even before a black hole forms in a gravitational system. In other systems with long range interactions, I have found that for general classes of theories, the local temperatures of various parts of the system are not equal at equilibrium. Some of these relations may have important applications in cosmology.

Foundations of quantum mechanics

"It is very difficult to be more interesting than quantum mechanics."
--Gaspar, to the frustrated wife of a physicist (who shall remain anonymous)

As a general rule, I am interested in understanding how one might be able to generalize our current laws of evolution and the state space these laws act on. This is not only to understand what other laws might be possible, but also to understand what is so special about current physical laws and states.

Other areas of interest, include for example, probabilistic interpretations of unitaries. In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. However, it turns out that one can also treat the evolution as being probabilistic in nature and one can measure `which evolution' happened.

I am also interested in the role of time in quantum mechanics, which was the subject of my Ph.D thesis. There, it was proposed that there is a new fundamental limitation on the accuracy of measurements of the time of an event. It is also impossible to tell the past from the future

This subject becomes particularly important in closed systems, and it is then that one encounters various issues which bear strongly on attempts to quantize gravity.