At the core of Quantum Information Science (QIS) is the idea that information processing is limited by the laws of physics that the carrier of information must obey. Most of today's information is encoded in a classical way, as the on/off of voltage in an electrical circuit for instance, or the point depth engraved on a CD. However, it is conceivable and increasingly realistic to encode information on genuinely quantum objects. For example the polarisation of a single photon, horizontal or vertical, is a way to encode a bit. The point of this is that quantum physics adds a new dimension to processing logic. The ability to bring a quantum object in two states at the same time, in superposition, was made famous by Schrödinger with his cat. Exactly this superposition can be used to perform a new kind of "coherent" information processing that results in the exponential power increase of a quantum computer over the classical one. Moreover, quantum objects can share correlations much stronger than their classical counterpart. This "spooky action" (Einstein) is known as quantum entanglement.

Part of our research is to clarify the role of entanglement in quantum computing. Specifically, we found that the computing power of correlations can be characterised using a novel framework. The framework describes how an external control computer can, by interacting with quantum correlated resource states, perform calculations beyond its own power. We also introduced a new programmable version for building a quantum computer. Ideally suited for experiments, Ancilla-Driven Quantum Computation (ADQC) requires only a single moving quantum system, the ancilla, and a single interaction.

An increasing part of our research is devoted to thermodynamics in the quantum regime, and the links between information theory and thermodynamics. We confirmed that while quantum entanglement is known to enable many counterintuitive effects, entanglement is not able to violate the second law of thermodynamics.
However, entanglement is not just a low temperature effect. In the right environment it can persist at high temperatures and even exists in biological systems, for instance, between the electronic clouds of DNA base pairs.

Currently we are working on characterising the behaviour of quantum systems in non-equilibrium. We are also involved in an experiment with a tiny nanosphere. 

Brief summaries of past and current research projects

Landauer's principle in the quantum domain 

In a recent paper we demonstrate the validity of Landauer’s erasure principle in the strong coupling quantum regime by treating the system-reservoir interaction in a thermodynamic way. We show that the initial coupling to the reservoir modifies both the energy and the entropy of the system, and provide explicit expressions for the latter for a damped quantum harmonic oscillator. These contributions are related to the Hamiltonian of mean force and dominate in the strong damping limit. They need to be fully taken into account in any low temperature thermodynamic analysis of quantum systems. A popular version of the paper is here.

Ancilla-Driven Quantum Computation (ADQC) 

ADQC is a new model of quantum computation that combines the advantages of gate-based and measurement-based quantum computation. ADQC is very well suited to experimental situations as it naturally uses static, long lived qubits as register qubits which are addressed sequentially by a flying, easy to manipulate qubit, called the "ancilla''. In each step the ancilla interacts with a fixed interaction, E, with a single register qubit or at most two, see Figure.  

After coupling the ancilla is measured in a suitable basis and this results in a back-action that, step by step, 'steers' the register's state. The interactions suitable for universal, stepwise deterministic ADQC are locally equivalent to the Ising model or the Heisenberg XX model with maximal coupling strength. Apart from unitary evolution, any generalized measurement can be implemented with the help of a second ancilla.

The architectural advantage of the model is that only the ancilla parameters, i.e. initial state and measurement basis, have to be manipulated, while the register itself is always only addressed with a single type of interaction. This is suited to many physical systems where the necessary register-ancilla interaction is available, such as neutral atoms in optical lattices, micro ion trap arrays, nuclear-electron spin systems and cavity QED-superconducting qubits. Besides, computations in the ADQC model can be translated into patterns for standard MBQC and vice versa. This implies the existence of a wider class of graph states for quantum computation, which includes so-called "twisted graph states"  generated from non-commuting coupling operations.

Bell-inequality test for a single massive boson

Experiments showing the violation of Bell inequalities have formed our belief that the world at its smallest is genuinely non-local. While many non-locality experiments use the first quantised picture, the physics of fields of indistinguishable particles, such as bosonic gases, is captured most conveniently by second quantisation. This implies the possibility of non-local correlations, such as entanglement, between modes of the field. In this paper we propose an experimental scheme that tests the theoretically predicted entanglement between modes in space occupied by massive bosons. Moreover, the implementation of the proposed scheme is capable of proving that the particle number superselection rule is not a fundamental necessity of quantum theory but a consequence of not possessing a distinguished reference frame.

Measurement-based quantum computation (MBQC)

Measurement-based quantum computation is an approach to computation radically different to conventional circuit models. Instead of processing information through a network of logical gates as in conventional circuit models, computation is implemented by a sequence of adaptive single-qubit measurements on a highly entangled multi-partite resource state.

Recently, we showed (here or here) that the GHZ states (Greenberger-Horne-Zeilinger) are sufficient resources to compute NAND gates in MBQC implying that the GHZ paradox is linked to universal classical computation. This solution is optimal within quantum theory as smaller resources would imply the existence of correlations of the artificial non-local boxes, a tool introduced to investigate non-local theories beyond quantum theory. 

In the speculative paper How much of one-way computation is just thermodynamics? (or here) we compare the process of measurement-based computing using the cluster state to the magnetisation process in the Ising model. Thermal equilibrium is defined by balancing two counteracting quantities, the energy and the entropy. A phase transition occurs when an ordered state of low entropy becomes permissible below a certain critical temperature. In measurement-based quantum computation, the transition from initial disorder, where no information about the result of the computation is known, to the unique result of the computation requires a sophisticated balance, too. The entanglement of the cluster state is comparable to the energy, while the possible outcomes of the computation correspond to entropy. During computation the entanglement is destroyed by carefully measuring the cluster state, thereby driving the ordering process. It is known that the Ising model cannot achieve order in 1D which, simply speaking, is due to the impossibility of having enough correlations reaching across the system. We argue that the same reasoning applies to the one-dimensional cluster state which is not a universal resource as it fails to produce the solution for arbitrarily large computations.

Thermal entanglement in quantum many-body systems

Harmonic Lattices 

Harmonic lattices are an important class of quantum many-body systems reaching beyond discrete systems and providing the tools to describe continuous systems such as trapped ions. Telling practically whether a state of a harmonic lattice is entangled was considered difficult and only sufficient criteria, such as a generalisation of the discrete PPT-criterion and the violation of entanglement witnesses, were known. 

In Entanglement and separability of quantum harmonic oscillator systems at finite temperature (or here) we establish a necessary and sufficient criterion for full separability for thermal equilibrium states of harmonic lattices. This implies a critical temperature below which entanglement is present and this threshold is vitally important for any experiments using entanglement. In a nutshell, the entanglement-separability crossover happens when the thermal energy is of the order of the energy of the strongest oscillation of the lattice. Interestingly, the manifestations of entanglement differ for various temperature ranges and can additionally be controlled by tuning external parameters as I have recently discussed in Thermal state entanglement in harmonic lattices (or here). 

General Models

In Macroscopic Entanglement and Phase Transitions (or here) we review recent research activities that establish the concept of entanglement at a macroscopic level. On the other hand a short overview is given, summarising the various order concepts known in condensed matter physics and used to describe phase transitions. Finally, we speculate whether entanglement could be a generalised order concept itself, relevant in (quantum induced) phase transitions such as BEC. 

In Survival of entanglement in thermal states (or here) we establish a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground-state entanglement. The relation can be used when only the ground state energy and the partition function are known. The condition is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Several examples are given allowing a characterisation of the minimum gapping behavior for the survival of entanglement in the thermodynamic limit.  

Quantum Fields

In Detecting entanglement with a thermometer (or here) we study the behaviour of the spatial entanglement in a non-interacting Bose-gas and find that it exists on a macroscopic level for low enough temperatures. We further show a correspondence of the critical temperature for the occurrence of a Bose-Einstein condensate  (BEC) and the temperature for the onset of entanglement which confirms the intuition that BEC requires entanglement.

In Spatial Entanglement From Off-Diagonal Long Range Order in a BEC  (or here) we quantify the spatial entanglement in an ideal bosonic gas around the transition temperature for condensation by probing the gas with two localised quantum harmonic oscillators. We show that spatial entanglement in the gas is directly related to the off diagonal long range order (ODLRO) of the system and hence to the onset of condensation.

Quantum Cryptography

We participated in the development of a fully tomographic quantum key distribution protocol that is unconditionally secure even when the channel noise rises above the trust-threshold of the standard BB84 protocol. A description of the Singapore protocol is here:  Highly Efficient Quantum Key Distribution With Minimal State Tomography .