Quantum Information GroupDepartment of Physics, The University of Tokyo

Research Introduction for Students

Quantum mechanics can be strange. It implies many counterintuitive phenomena, which can at first be hard to believe. The Danish physicist Niels Bohr is famously quoted as saying “Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it”.

In recent years, some of these strange phenomena have been used in information processing, giving the ability to perform tasks which are impossible by traditional, classical information processing — such as absolutely secure communication in quantum cryptography, teleportation and super-dense coding. Such protocols are known collectively as quantum information processing (QIP).

The great breakthrough made in the last 20 years, which has made this possible, is the recognition that information is physical. That is, the laws and equations that govern the flow of information depend on the physics of the system used to carry that information.

For example, imagine two people using flash lights to communicate using Morse code. If two atoms tried to do Morse code using individual photons (where quantum mechanics becomes important), things could quickly get weird and stop working. Amazingly, the strange behaviour we see in quantum mechanics can be used to our advantage and gives rise to QIP.

One of the main quantum effects which leads to some of the enormous benefits in QIP is entanglement (referred to by Einstein as “spooky action at a distance”). In this group we research entanglement and its role in QIP, in various different aspects. We outline the main topics of our work below.

Restrictions of acting locally

Consider a quantum system made of many separate systems; these systems may be separated into different laboratories. If we restrict ourselves to acting separately on each system (in each lab), we will find that we cannot do as much as if we could act on them all together in the same place. This is still true even if we allow the systems to communicate classically (like each lab having internet or phone connections).

The situation described above is called “Local Operations and Classical Communication” (LOCC) and is a crucial concept in quantum information theory. It is implicit in how we define entanglement (entanglement is essentially defined as a quantity on a quantum state which does not increase under LOCC). It is also commonly the situation we consider in quantum cryptography — instead of separate labs we may consider separate banks using quantum systems to transfer important, and so secret, information.

It is notoriously difficult to characterise LOCC operations completely in a mathematical way. We therefore often consider the restriction of LOCC case by case. In our group, we consider how LOCC restricts what measurements we can perform.

Measurements are the way in which we go from a quantum state to classical information — they are how we “decode” the quantum state. Thus they are crucial to any quantum readout of information, and indeed to many quantum information processing protocols. The restriction of LOCC is of crucial importance when considering networks of individuals, and is also important in notions of locality.

Two problems we specifically consider in this group with regard to LOCC measurements are local state discrimination (given a set of possible candidate states, our task is to tell which one we are given by LOCC measurement) and local copying (given a state, we wish to copy it optimally locally). These problems are quite general and have implications in many scenarios in quantum computing as well as notions of locality.

We have recently shown that entanglement gives a quantitative bound on how well it is possible to discriminate states by LOCC measurements [1]. We have also investigated local copying, showing examples of when it is and is not possible, and its relationship to LOCC state discrimination [2]. We continue to study the restrictions of LOCC on measurements and other quantum information tasks, and how these can be used to give new quantum information protocols.

Entanglement

Entanglement is an essential resource in quantum information. More recently it has been recognised as having a role in many solid state systems and critical phenomena too (see the last section).

When considering infinite dimensional systems there are subtleties that do not exist in the finite dimensional case, and entanglement too can behave in a strange way. We look at the effect of dimension on entanglement: how infinite dimension can give rise to different kinds of entanglement (e.g. [3]), and how we can use subtleties of dimension to help us generate and manipulate entanglement (e.g. [4]).

In the multiparty case, things get similarly complicated. There is the possibility of many different kinds of entanglement, and it can even be difficult to define entanglement well. We investigate entanglement in many body systems, and how it can be related to operational quantum information tasks.

One-way quantum computing

Quantum computers promise amazing performance, enabling certain problems to be solved with exponential speed up over their classical counterparts. One of these problems is factorising large numbers, which is crucial to much of today’s internet security. A quantum computer could do this very quickly and would render much current cryptography insecure — this is also a big reason why quantum cryptography has become so popular.

One of the major problems in building a quantum computer is the sensitivity of quantum systems. Any system we would use to perform our computation would be subject to interactions with its environment, and these interactions can destroy the quantum state, rendering computation impossible (a process known as decoherence).

One-way quantum computation was invented to deal with this problem. Instead of keeping the quantum states all the way through the computation, we measure them earlier on. This has the effect that the computation is no longer reversible — since measurements are irreversible — hence the name one-way computation.

It is presently not too clear what the exact difference between one-way quantum computation and normal unitary quantum computation is. In this group we investigate this difference: the exact conditions, on the entanglement of the systems at hand and elsewhere, allowing quantum one-way computation, and other related questions.

Entanglement in physics

In the last few years it has become clear that, as well as its importance in quantum information, entanglement occurs in much of general physics as well. Multiparty entanglement is present in many ground states of condensed matter physics, has been associated with critical phenomena in solid state physics, and also plays a role in symmetry breaking in high energy physics.

These recent discoveries come with a plethora of new questions. How common is the occurrence of entanglement in these systems? What is the role of entanglement in critical phenomena?

In our group we investigate the presence of entanglement in complex systems in thermodynamic equilibrium, and search for the answers to these and other related questions.

By Damian Markham

For a more detailed summary of our current work, please see the Research page.

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