Characterizing Nonclassical Correlations via Local Quantum Uncertainty

Abstract

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2 x d systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the 'discord' type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.Comment: Published in PRL, Editors' Suggestio

Quantum coherence and uncertainty in the anisotropic XY chain

“…Due to the fact that the systems we consider in our work are invariant upon exchanging two spins, the LQC remains also unchanged. Another related concept is the LQU, which is a full-fledged discordlike family of measures of purely quantum correlations [21]. In fact, LQU is merely an optimized version of the LQC over all possible local observables, that is,…”

“…We also find out that although this simpler alternative still spotlights the CP of the QPT, the factorized ground state can no longer be detected in this setting. Moreover, by studying a novel quantum correlation measure, namely local quantum uncertainty (LQU) [21], which is closely related to LQC, we discuss the consequences of the optimization involved in the evaluation of this measure for the identification of the CP and FP. Our results show that there exist nonanalyticities appearing in LQU that in fact do not correspond to any critical behavior.…”

Witnessing Multipartite Entanglement by Detecting Asymmetry

“…These results paved the way for investigating the link between coherence and quantum properties of multipartite systems. In particular, the relationship between coherence and quantum correlations has been explored [6,9,13,16,18,19,23,24].…”

“…Yet, to date, there is no operational interpretation for such definition of coherence. A concurrent body of work has linked the coherence of ρ in a basis {h} to the degree of uncertainty in a measurement of an observable H = ∑ h h|h h| on ρ [2][3][4][5][6][7][8][9][10][11][12][13]. Such genuinely quantum uncertainty is due to the non-commutativity between state and observable.…”

“…In this context, the degree of coherent superposition of a state ∑ i c i |i i|, ∑ i |c i | 2 = 1, i.e., coherence (we omit the quantum label, from now on) in a reference basis {i}, is a resource. The crucial question is to determine how to obtain a computational advantage powered by coherence [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The coherence of a finite-dimensional quantum state ρ has been defined as its distinguishability from the sets of states which are diagonal in a given basis [14][15][16][17][18][19].…”