Local transformations of multiple multipartite states

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.

Phase estimation of coherent states with a noiseless linear amplifier

Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.