## Popular Articles

**Uncertainty and nonlocality**: a description of my paper with Stephanie Wehner, Science 2010.**Quantum information can be negative**: an accessible description of my paper with Horodecki and Winter in Nature.**Sending quantum information down channels which cannot convey quantum information**: A perspective in Science. A copy is available here.**Quantum computing as free falling**: A Science perspective on quantum computation as geometry. A copy is available here.

## Research Interests

I am currently engaged in research projects in several fields. I am particularly interested in quantum information theory, quantum gravity, black hole thermodynamics, and foundations of statistical mechanics, thermodynamics and quantum theory. Although these fields are often distinct, there are many conceptual overlaps, as can be seen below.## Selected publications

- J. Oppenheim and S. Wehner, "The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics", Science 330:1072-1074 (2010)
- M. Horodecki, J. Oppenheim, A. Winter, "Partial quantum information", Nature 436:673-676 (2005)
- K. Horodecki, M.Horodecki, P. Horodecki, J. Oppenheim, "Secure key from bound entanglement", Phys. Rev. Lett. 94, 160502 (2005)

## Quantum information theory

*"You don't understand quantum mechanics, you just get used to it."*

-- attributed to Feynman, borrowed from von Neumann.

-- 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."

--Confucius

especiall if there is no cat."

--Confucius

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. A recent project has been in 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.

## Statistical Mechanics and Thermodynamics

*"In this house, young lady, we obey the laws of thermodynamics!"*

--Homer Simpson

--Homer Simpson

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)

--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.