We address estimation of one-parameter qubit gates in the presence of phase diffusion. We evaluate the ultimate quantum limits to precision, seek optimal probes and measurements, and demonstrate an optimal estimation scheme for polarization encoded optical qubits. An adaptive method to achieve optimal estimation in any working regime is also analyzed in detail and experimentally implemented.
We study gap solitons which appear in the topological gap of 1D bosonic dimer chains within the mean-field approximation. We find that such solitons have a non-trivial texture of the sublattice pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in presence of a localized energy potential. PACS numbers:Topologically non-trivial structures are currently in the focus of attention of scientific community. Topological insulators are studied in electronic systems for fermionic particles [1], but also in analog systems for bosonic particles (atomic lattices and photonic "topological mirrors" [2][3][4][5][6][7][8][9]). The advantage of artificial photonic systems lies in their design flexibility and the possibility of direct wavefunction measurements. The properties of such structures are relatively well explored in the linear regime, where the topological invariants have been found to characterize the bands [10] and determine their properties, including the existence of chiral edge states [11]. The nonlinear regime is much less explored. Indeed, an interacting quantum fluid exhibits topological properties on its own [12], and one can expect them to become even richer when combined with the topology of the dispersion in the linear case [13][14][15][16][17][18].A 1-dimensional (1D) periodic lattice with a certain degree of dimerization is one of the simplest lattices exhibiting topological properties [19][20][21]. Such structure shows a splitting of a single s-type band into two bands, corresponding to the bonding and anti-bonding states of the individual dimers. These subbands are separated by a gap, characterized by a topological invariant -the Zak phase [22]. The properties of nonlinear solutions existing in this gap -the gap solitons -can be expected to be strongly modified with respect to the solitons in the ordinary gap. The Su-Schrieffer-Heeger soliton is perhaps one of the most famous examples of topologically nontrivial solutions [23] for a dimer chain. However, it involves dynamical dimerization, that is, modification of the properties of the lattice itself: this soliton is a domain wall between two distinct lattices. Similar dimerization domains can be observed in ionic chains [24, 25] and artificially created in photonic chains [26]. Recently, chiral solitons of the SSH type were observed in double chains [27]. But there also exist solitonic non-linear solutions that do not require the modification of the lattice. Many of them have been studied in dimerized and zigzag lattices in acoustics [28], Bose condensates [29], and photonic systems [30][31][32][33] (including PT-invariant ones [34][35][36][37][38]), with a particularly interesting recent experimental observation [39]. However, the crucial role played by the anisotropy of the Bloch part of the soliton wave function with respect to the two different atoms forming the lattice (and defining the sublattice pseudospin) has remained unnoticed.In this work, we demonstrate that a gap soliton in a single dimer chain can...
We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single-and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure. Bayesian inference is employed and compared with the ultimate quantum limits to precision, taking into account the biased nature of Bayes estimator in the non asymptotic regime. Besides, through the evaluation of the asymptotic a posteriori distribution for the gate parameter and the comparison with the results of Monte Carlo simulated experiments, we show that asymptotic optimality of Bayes estimator is actually achieved after a limited number of runs. The robustness of the estimation procedure against fluctuations of the measurement settings is investigated and the use of entanglement to improve the overall stability of the estimation scheme is also analyzed in some details.
We address quantum communication channels based on phase modulation of coherent states and analyze in details the effects of static and dynamical (stochastic) phase diffusion. We evaluate mutual information for an ideal phase receiver and for a covariant phase-space-based receiver, and compare their performances by varying the number of symbols in the alphabet and/or the overall energy of the channel. Our results show that phase communication channels are generally robust against phase noise, especially for large alphabets in the low energy regime. In the presence of dynamical (non-Markovian) noise the mutual information is preserved by the time correlation of the environment, and when the noise spectra is detuned with respect to the information carrier, revivals of mutual information appears.
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