Probabilistic metrology or how some measurement outcomes render ultra-precise estimates

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision that exceeds the deterministic bounds for the average precision. This establishes a new ultimate bound on the phase estimation precision of particular measurement outcomes (or sequence of outcomes). For probe systems subject to local dephasing, we quantify such precision limit as a function of the probability of failure that can be tolerated. Our results show that the possibility of abstaining can set back the detrimental effects of noise.Comment: Improved version of arXiv:1407.6910 with an extended introduction where we clarify our approach to metrology, and probabilistic metrology in particular. Changed titl

Beating noise with abstention in state estimation

We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consists of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal such protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are exemplified for small values of N. For asymptotically large N, we derive analytical expressions of the fidelity and the probability of abstention, and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback-Leibler (relative) entropy. As a byproduct, we obtain an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides a most significant improvement as compared to the standard approach

Entanglement assisted alignment of reference frames using a dense covariant coding

We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed.Comment: 4 pages, RevTeX, Version to appear in PR

Frustrated magnetism and caloric effects in Mn-based antiperovskite Nitrides : Ab Initio theory

We model changes of magnetic ordering in Mn-antiperovskite nitrides driven by biaxial lattice strain at zero and at finite temperature. We employ a non-collinear spin-polarised density functional theory to compare the response of the geometrically frustrated exchange interactions to a tetragonal symmetry breaking (the so called piezomagnetic effect) across a range of Mn3AN (A = Rh, Pd, Ag, Co, Ni, Zn, Ga, In, Sn) at zero temperature. Building on the robustness of the effect we focus on Mn3GaN and extend our study to finite temperature using the disordered local moment (DLM) first-principles electronic structure theory to model the interplay between the ordering of Mn magnetic moments and itinerant electron states. We discover a rich temperature-strain magnetic phase diagram with two previously unreported phases stabilised by strains larger than 0.75\% and with transition temperatures strongly dependent on strain. We propose an elastocaloric cooling cycle crossing two of the available phase transitions to achieve simultaneously a large isothermal entropy change (due to the first order transition) and a large adiabatic temperature change (due to the second order transition)

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of $N$ spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.Comment: 4 pages, RevTex, final version to appear in Phys.Rev.Let