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QUANTUM REFERENCE FRAMES
It is common in quantum mechanics to assume
that clocks and rulers – “reference frames” with respect to which we measure all systems
are perfect, and classical – i.e. large. We have
been researching how to treat them in the
quantum mechanical formalism and see what
type of limitations doing this does or does not
impose. This has interesting foundational issues
in understanding quantum space and time in
extreme conditions such as near black holes.
A comparison of probability of success for obtaining the
However it also is important for building ideal measurement result in three different cases of a small
quantum information processing devices! For quantum reference frame. The dashed line corresponds to
quantum computers the reference frames take the case of sequential measurements without any
correction, the dashed-dotted line is for the case in which
the form of lasers, and we want to use as small we correct the measurement result via applying unitary
and weak lasers as possible, to miniaturize the interactions after any two measurements and the solid line
belongs to the case of correction via applying corrections
devices.
after specific outcomes are obtained.
Currently we are focusing on a program of
research initiated by Dr. Rudolph and colleagues concerning how long a quantum reference frame
(QRF) lasts if it is used as a resource for performing quantum operations and also how we can make it
to last longer. The special case that we are looking at is the effect that the measurement of the angle
between a directional quantum reference frame and a spin-1/2 particle has on the ability of QRF to
act as a reliable reference for future measurements. We show that each time one of these spin-1/2
particles is measured against the QRF, it causes the reference frame to suffer from a back-action
which makes the probability of getting the correct measurement result decrease as the number of
measurements increases. We recently have found two different ways of fighting this seemingly
inevitable degradation – either through an active corrective mechanism, or by a careful monitoring of
the dynamics involved. In the figure below, we can see how these two ways of fighting the
degradation of the QRF makes it useful for a larger number of measurements.
TIME AND THE SECOND LAW OF THERMODYNAMICS
Time is one of our most ancient mysteries,
while in stark contrast it is only in the past
century that we have become aware of the
quantum mechanical properties of Nature.
Why do events seem to flow past us only in one
direction? Why do we only know the past and
not the future? Why do all parts of the universe
experience the same Arrow of Time?
While these questions may seem better suited
to a philosophy department, central to all these
deep and significant questions is the notion of
“information”, and within the field of Quantum Information Theory we are applying recent
discoveries in the theory of quantum entanglement to better understand how Time works, and how
entanglement in an actual physical system can be used to bend or even reverse the Arrow of Time!
Beyond being of foundational importance, the research also offers practical insights into the
fundamental limits in the efficiency of thermodynamic engines, and into how heat flow and energy
transfer in quantum systems can be modified and controlled via quantum correlations. We were
recently by Scientific American to comment on a provocative proposal by Maccone - our
understanding of this issue allowed us to identify the flaw in his proposal [Physical Review
Letters,104,148901], and to subsequently undertake a thorough analysis of the time reversals
possible due to quantum entanglement http://arxiv.org/abs/1002.0314.
CLASSICAL NOTIONS IN A QUANTUM UNIVERSE
Quantum Mechanics encompasses not only the strange
particle world of atoms, photons and quarks, but also the
more familiar classical world of galaxies, stars, trees and
humans. How our classical notions fit into the counterintuitive world of Quantum Mechanics is far from being a
trivial question and brings with it delicate technical
challenges and a greater mastery of how quantum
information behaves. We are currently conducting research
on how classical correlation patterns fundamentally fit into
the underlying quantum world and asking the surprisingly difficult question:
How much classical correlation can we create in the simplest setting of two fundamental particles?
Our interface with the quantum world is ultimately classical, so beyond its foundational importance,
understanding how traditional classical information relates to quantum information is significant for
the manipulation of quantum systems and for information processing tasks. We have recently solved
this problem for a variety of special cases, and are now focussed on obtaining a fully general
solution.
RELATIVISTIC QUANTUM INFORMATION THEORY
When we combine Relativity with Quantum Mechanics we
are inexorably lead to the notion of a quantum field.
Currently quantum field theories in the setting of curved
spacetimes are pushing the frontier of our understanding of
the laws of Nature. In recent times we have come to realise
the important role that certain information theoretic
notions play at this frontier. The most famous being the socalled Black Hole Information Paradox, which asks whether
information is truly destroyed in the most extreme
conditions of a black hole. Relativistic Quantum Information
Theory seeks to investigate at a fundamental level, how does information behave in the presence of
gravity and at velocities close to the speed of light. Two such questions of interest for us are:
How does vacuum entanglement relate to the causal structure of a spacetime? How are global
spacetime properties encoded in the local state of a quantum field that we access with a particle
detector? For many years the question has been open of whether the relativistic version of quantum
information theory is different with respect to fundamental information processing power from nonrelativistic quantum information theory. By considering these foundational questions we have
recently managed to show that certain important cryptographic protocols – such as “secure
gambling on the quantum internet” are possible only in relativistic quantum information theory, a
result which may lead to many new practical uses for quantum communication theory.
ROBUST COMPUTERS MADE OF LIGHT
A
quantum
paradigm
for
information
promises
more
reliable
communications
and
enhanced algorithms for many
important problems, such as
quantum chemistry leading to
better drug design, simulation of
light harvesting complexes leading
to better solar cells or design of
new exotic materials capable of
withstanding extremes such as
heat, pressure or electrical current.
One of our areas of research in the IMS group is trying to bring the quantum computer closer. Our
focus is on optical and solid state (semiconductor)
systems. Recently [Phys. Rev. Lett.103, 113602 (2009)]
we proposed a device at the interface of these two
technologies – a “quantum dot machine gun” for
entangled photons. This idea captured some media
attention and is currently being pursued by three
different experimental groups. Even having such a device
we still need a robust way of computing with it. To this
end we have been investigating how it could be used in a
so-called “fault tolerant one-way quantum computer”, a
model in which one starts with a three-dimensional
lattice of correlated quantum bits and then measures them out following an order dictated by the
quantum algorithm, in such a way that the
overall shape of the resulting lattice will
enact a series of quantum logical gates. We
have proposed a way of building of this
lattice using arrays of quantum dots – tiny
pyramidal structures that are able of firing
correlated photons - linear optical gates
and very efficient detectors. All these
components offer very good controllability
and scalability. Simulations have been
carried out which suggest that our proposal
would be quite robust against errors in the Schematic setting of our proposal: An array of quantum dots
(purple) fire strings of photons which at a later stage are
quantum dots, the optical gates and in the combined in the optical gates to create correlations between
parallel beams (yellow vertical lines). This constitutes the
detectors.
substrate
ON-CHIP PHOTONIC NETWORKS
With recent advances in fabrication techniques, scientists have been able to make devices that
manipulate light at smaller and smaller scales. This has opened up the possibility of information
processing with light at the nanoscale. Here, the new field of nanophotonics promises high
bandwidth, high speed and ultra-small scalable components. Within the Controlled Quantum
Dynamics group we are actively pursuing research in
into quantum-controlled devices based on the
potential offered by nanophotonics. One of the main
topics we are investigating is the use of
measurement-based quantum control, a new
paradigm for controlling quantum systems. Here, the
networking of fundamental on-chip components is
employed in systems such as photonic crystals, atom
chips and photonic waveguides (see Fig. 1). By
On-chip network of photonic waveguides
performing complex mathematical simulations we are
generating entangled resource states for
developing devices for deployment in applications
measurement-based quantum control.
such as quantum communication and quantum
computing. These applications offer far superior performance compared to their non-quantum
counterparts. In addition to this applied research, we are also investigating scenarios in which novel
physical effects such as quantum phase transitions, chaotic dynamics and the creation of
multipartite entangled states arise. The goal is to probe the foundations of quantum physics and find
new ways to harness quantum effects for efficient and scalable on-chip quantum information
processing.
NONLINEAR QUANTUM OPTICS WITH NANOSTRUCTURED MEDIA
An active area of our research is the generation of large nonlinear
effects at the quantum level – a field in which Imperial researchers
have been leading the world for many years. A major problem for
quantum information processing is that photons interact very
weakly with each other. If large nonlinear effects become possible
in the single-photon regime, it will allow the efficient production
of entangled states, the generation of nonclassical states such as
Schrödinger cat states, and the processing of quantum
information encoded into continuous and discrete variables. To
tackle this problem we consider surface plasmon polaritons (see
Efficient single-photon excitation
figure), an exotic form of light (photons) coupled to matter
of on-chip surface plasmon
(electrons), where it has recently been recognised that they
polaritons
using
attenuatedprovide the potential for achieving large nonlinear effects with
reflection geometries.
deep sub-wavelength field confinement in nanostructured media.
We are working on developing efficient nonlinear plasmonic waveguides and investigating coupled
nonlinear plasmonic systems. The proposal of experimentally realisable schemes for plasmonic
quantum control and information processing is one of our major goals. Mathematical modelling and
careful application of quantum optics theory is essential in our research on this topic.
PEEKING INSIDE THE QUANTUM BOX: INDIRECT SYSTEM THEORY FOR MANY-BODY
HAMILTONIANS.
Estimating the nature and strength of interactions
has been one of the main goals in quantum
theory for almost a century. But it is only now
that we are capable, in principle, of
experimentally identifying the specific individual
interactions – so called “Hamiltonians” of large
systems of particles. However; in general the
complexity of such Hamiltonian estimation is vast,
as each particle needs to be initialised and its
dynamics monitored. In collaboration with RIKEN,
Japan, we have discovered efficient methods for
estimating certain types of interactions often
encountered in experiments. These can be
identified indirectly- by only monitoring the quantum dynamics of the surface of the system, the
inner dynamics is revealed. This is analogous to tomography as used in, e.g., seismology and
ultrasonography. Our results provide further evidence for a “holographic principle” of many-body
Hamiltonians, which was previously conjectured by our group based on the scaling of entanglement
in these systems.
TOPOLOGICAL ORDER, QUANTUM ERROR CORRECTION AND FAULT TOLERANT QUANTUM
COMPUTING
The ability to store and process quantum states is key to the nascent field of quantum information
technology. However, quantum information is delicate. It can be corrupted by imperfect control of
the 'knobs' accessible to the experimentalist, or by
unwanted coupling to other systems.
One of the most important discoveries in quantum
information in the last 15 years was the discovery of
methods to protect quantum information from noise, and
also to process the resulting protected states. Two main
approaches have been developed - one based on the use of
quantum generalizations of error correcting codes, the
other based on a newly discovered property of matter
known as 'topological order': topologically ordered systems
can protect quantum information without active error
correction.Within the CQD program we are currently
studying an approach to protecting and coherently
processing quantum information which combines both of
A topological fault tolerant quantum computing these approaches. Two recent breakthroughs in the group
scheme that can tolerate significant loss errors.
have concerned the effect of a particular type of error
where
the
information
carrying entity (which could be
an atom, photon, or solid state
device) is completely lost. We
have shown that certain error
correcting codes can tolerate
loss of up to half of their
quantum bits, while still
retaining the ability to correct
for other types of noise [Phys.
Rev. Lett. 102, 200501 (2009)].
Secondly, we have shown that
Error threshold tradeoff curve for topological fault tolerant quantum computing
scheme, determined by Monte-Carlo simulations. Horizontal axis: loss error
a quantum computing scheme
probability per qubit. Vertical axis: computational error probability. The large
using such topological codes is "correctable" region indicates that the practical realisation of quantum computing
also robust to loss errors at may be much easier than hitherto expected.
rates of up to 25 percent. These
schemes, exhibiting very high thresholds that are comparable with state of the art experiments,
indicate that the practical realisation of quantum computing may be much easier than hitherto
expected.
DISTRIBUTED MEASUREMENT BASED QUANTUM COMPUTING
A significant problem in building a quantum computer is the seemingly contradictory requirements of
having well isolated physical systems (qubits) that can be independently addressed, while at the
same time having the qubits interact strongly with each other in order to build up quantum
entanglement - the key resource that enables the power of a quantum computer.
One of the most significant contributions of CQD group members was to propose a scheme for
distributed quantum computation that overcomes this contradiction: we showed that distant qubits
can be entangled via single photon interference effects and photodetection, in such a way that a
large scale quantum computer can be constructed. This work has had significant impact on the field,
with both extensive further theoretical work (within the group and elsewhere) as well as
experimental demonstrations of the core components of the scheme. Within the group, we have
recently examined the effect of noise in quantum dot based implementations, and also shown that
the idea can be made to work using the rather more mature technology of gas vapour cells.