Topics in the Theory of Entanglement
The following areas are all the subject of study by researchers in the Institute of Mathematical Sciences at ICMST (Imperial)
1 Fundamental Theory of Entanglement:
We will continue our exploration of scaling laws in quantum many body systems, notably area laws that we have pioneered (see IRC Highlight: Entanglement and Area). The exploration of such scaling questions is important as they allow us to gain insight into the complexity of the description of typical states of quantum many body systems. Understanding the impact of such scaling laws is important when trying to devise new methods for the efficient approximation of quantum states of many body systems, see eg Anders, Plenio, Dur, Verstraete & Briegel, PRL 2006. Surprisingly perhaps, in recent work with IRC postdoc Shashank Virmani (who will move to U of Hertfordshire) we have also realized that these scaling laws are important as well in a connection between many body systems and channels in which errors between successive transmissions exhibit correlations (quant-ph/0702059). All channels are, strictly speaking, memory channels and this feature becomes increasingly important with increasing transmission rates e.g. in photonic quantum communication.
2 Quantitative entanglement witnesses
As the number of entangled qubits increases it becomes essential to avoid scaling up full tomography to quantify the entanglement and in fact any other physical quantity that is not directly accessible to measurement (Purity, Gaussness of states, …). We have previously developed such approaches for entanglement and are planning to extend these ideas in various directions. This approach may lead to considerable reductions in experimental resources. For each experiment the best observables for measurement and the appropriate data analysis methods, need to be identified. For other physical quantities these methods may have to be varied. Furthermore, a general framework for the quantification of physical properties based on limited measurement data needs to be developed.
3 Measurement-based quantum dynamics
In recent work I have explored the dynamical properties of entanglement in random processes a problem that has both fundamental interest but may also be of use in algorithms that rely on random quantum states. See eg Oliveira, Dahlsten & Plenio, PRL 98, 130502 (2007) and Dahlsten, Oliveria & Plenio, quant-ph/0701125. Natural implementations of such random processes where the randomness is not imposed by the experimenter (and therefore derived from some classical pseudo random number generator) have however been missing. We have now realized that the weighted graph states that we have used in the simulation of quantum systems provide a natural system in which to carry out such simulations as in these the randomness is imposed by quantum mechanics. We are planning to explore both the theoretical properties of the so gained specific random processes and will explore in detail the implementation of the required weighted graph states in experiments.
4 Entanglement dynamics in coupled micro-cavities
Arrays of cavities, each interacting strongly with atoms, are currently the subject of tremendous experimental progress. This gives rise to a new class of quantum optical systems in which networks of individual atoms or atom clouds can be strongly coupled to quantised modes of light. We have pioneered recently the realization that such systems can be used as quantum simulators with realistic, existing, parameters (see IRC highlight Quantum phase transitions of polaritons in arrays of coupled micro-cavities and Hartmann, Brandao, Plenio, Nature Physics 2, 849 (2006). In our future work we are planning to study the novel possibilities offered by these devices for the generation and manipulation of entanglement and the creation of locally addressable, effective many-particle Hamiltonians. This study is intended to pave the way towards the application of such devices as quantum simulators.
For further information contact Martin Plenio