Research projects
Quantum information theory in curved space-times and non-inertial relativistic frames of reference
Big question: It is not known how even to define a qubit in a curved spacetime, therefore it is not clear which of the fundamentally important quantum-informational quantities, have fundamental or absolute meaning in the presence of gravity. What is therefore the framework of quantum information in general relativity?
Basic idea: We have studied the notion of entanglement shared between two parties, when one of them is non-inertial (which, locally, is equivalent to the presence of the gravitational force). It has been found that the entanglement is not an observer-independent quantity and crucially depends on the motion of the reference frame.
Reference: D. E. Bruschi, J. Louko, E. Martin-Martinez, A. Dragan, and I. Fuentes, The Unruh effect in quantum information beyond the single-mode approximation, Phys. Rev. A 82, 042332 (2010).

Practical use of exotic relativistic quantum effects
Big question: Can the Hawking radiation or Unruh effect not only be measured and studied, but also used for practical purposes?
Basic idea: We show that a single point-like quantum particle can be used to determine absolute acceleration of its reference frame by local measurements on a quantum field. We find that this is only possible by measurements on highly excited massive fields, which reveals a special role played by the field mass in (general) relativity.
Reference: A. Dragan, I. Fuentes, and J. Louko, Quantum accelerometer: distinguishing inertial Bob from his accelerated twin Rob by a local measurement, Phys. Rev. D 83, 085020 (2011).

Entanglement of vacuum
Big question: How much entanglement can be extracted from vaccum? Or perhaps is the vacuum state an infinite reservoir of entanglement?
Basic idea: We study entanglement swapping between the vacuum state and a pair of accelerated point-like particles in an analytical, non-perturbative model of single-mode interaction.
References: A. Dragan, J. Doukas, E. Martin-Martinez, and D. Bruschi, Localised projective measurement of a relativistic quantum field in non-inertial frames, arXiv:1203.0655 (2012); A. Dragan, I. Fuentes, Probing the structure of vacuum entanglement, arXiv:1105.1192v1 (2011).

Black hole information loss paradox
Big question: It has been suggested that information can be destroyed in the process of evaporation of black holes. Can the total information be defined as a preserved quantity and under what circumstances?
Basic idea: With the use of a toy-model of evaporating black hole we show that the energy contribution to the radiated flux of Hawking particles must originate from the region of spacetime outside the never-to-be-formed event horizon. Therefore it is pointless to argue about the loss of information without taking into account the back-reaction between the radiation and the collapsing matter.
Reference: A. Dragan, Debunking the black hole information paradox, arXiv:1003.0094 (2010).

(In)validity of super-selection rules
Big question: Super-selection rules stating that superposing of certain physical quantities, such as electric charge is not allowed. Consequently no superposition of electron numbers is possible, while it is perfectly allowed to superpose number of photons. Does this rule hold and how can it be verified? What is the origin of this interesting principle?
Basic idea: Interference effects of states with no superpositions of particle numbers (Fock states) lead to practically indistinguishable consequences from the result of interference of superposed coherent states. This leads to the question, is it possible to verify the (in)validity of super-selection rules for massive particles at all?
Reference: A. Dragan and P. Zin, Interference of Fock states in a single measurement, Phys. Rev. A 76, 042124 (2007).

Non-locality and non-determinism of quantum mechanics and their relation to special relativity
Big question: It is known not only that non-locality of quantum mechanics is self-consistent with relativity, but these two theories coexist and fit amazingly well. Is this just a coincidence and is the approach of quantum field theory the only way of marrying quantum mechanics with special relativity?
Basic idea: We show that the Principle of Relativity involving all, not only subluminal, inertial frames leads to the disturbance of causal laws in a way known from the fundamental postulates of Quantum Theory. We show how quantum indeterminacy based on complex probability amplitudes with superposition principle emerges from Special Relativity.
Reference: A. Dragan, Why devil plays dice?, arXiv:0806.4875 (2008).