Transformações de estados e medições sequenciais: uma proposta experimental

Abstract

State transformations in quantum states are important and necessary for experimental implementations of quantum computation protocols and for realizations of experiments on foundations of quantum theory. Being capable of doing quantum operations in the laboratory gives one the possibility to make sequential measurements, which brings out new possibilities for applications and conceptual studies of this theory. Depending on which degree of freedom the quantum state is encoded, the experimental implementation of the transformation can change substantially. In the case of photonic qudits, spatial degrees of freedom have been used, as photon paths or slit states. For states encoded in photon paths any unitary can be implemented by interferometers, in principle. However, this method it is not automated, and that makes it difficult to change the implemented operation in a practical way. In the case of slit states as spatial degree of freedom to encode qudits, the use of spatial light modulators to prepare or operate on the states makes it possible to automate transformations. On the other hand, it has been a challenge to implement transformations that are not described by diagonal matrices. In this context, the question that this work tries to answer is how to make automated state transformations on spatial photonic qudits. We present an experimental proposal that is capable to do so, using a phase-only spatial light modulator (SLM) and interferometers, acting on states encoded in attenuated parallel Gaussian beams. The key point of our proposal is that implemented operation is entirely dependent on the phase modulation of the SLM, which guarantees that the transformation is automated. We have studied the limits in which this proposal can implement projections and permutations and describe the elements of POVM that can be accounted to with the proposed setup. We discuss theoretical limitations and possibilities, as so as approximations that may be important to guarantee in the laboratory such that the proposal can be correctly implemented. We also give preliminary experimental results with non-attenuated Gaussian beams. These results show good qualitative agreement with the theoretical predictions, suggesting that the proposal is feasible.