Abstract Recently, local quantum uncertainty (LQU) as a measure of quantum correlations has been proposed by Girolami et al . We here have investigated the LQU dynamics in a pair of qubits system subjected to either local or collective classical phase noises. The explicit analytical expressions of LQU for the two-qubit system of interest initially in a Werner state under these dephasing noises have been derived. We compare the dynamics of LQU with that of entanglement as measured with concurrence. Our results show that LQU always decays asymptotically while the entanglement displays sudden death phenomenon. Besides, there is no simple relation between the LQU and entanglement since LQU may be smaller or larger than entanglement. Finally, we try to protect LQU against the dephasing noise by means of filtering operation.
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given
k-partition of a
d-dimensional multipartite system, we introduce the total uncertainty as the sum of the uncertainties associated with all possible tensor products of local
SU(N) observables, where each observable acts on the corresponding subsystem. We show that the total uncertainty exactly equals the algebraic sum of the global state purity and the purities of all possible state reductions. For systems containing at least one single-qubit subsystem, this equality implies saturation of the Robertson-Schrödinger uncertainty inequality, with the missing term needed for saturation equal to the bipartite qubit-environment entanglement for a pure global state, or to the qubit two-Rényi entropy for a mixed global state. Leveraging on these results, we show how for any finite-dimensional multipartite system the Hilbert-Schmidt squared norm of the correlation matrix
t can be expressed exclusively in terms of the global and reduced state purities. We then derive a correlation matrix-based necessary condition for
k-separability of arbitrary finite-dimensional quantum states and show, in the case of
n qubits, how it is related to a necessary criterion for Bell nonlocality in scenarios with two dichotomic measurements per party. For sufficiently large systems the purity-based formulation of the
k-separability criterion always yields an exponential advantage over the direct evaluation of the
t-matrix norm, allowing for a more efficient practical verification of multipartite entanglement and nonlocality via simple experimental schemes based on purity measurements. Our results shed some further light on the intimate and intricate relation between correlations, entropies, uncertainties, and the entanglement certification and detection problem.
We develop a general perturbation theory for the local quantum uncertainty (LQU), a discord-type quantifier of nonclassicality based on the Wigner-Yanase skew information. Starting from a perturbed density matrix
ρ=ρ0+ερ1,we derive an explicit first-order expansion of
ρ1/2 using an integral representation based on the gamma function, and reduce the LQU optimization to the diagonalization of a
(d12−1)×(d12−1) matrix
w=w0+w1 defined in terms of the
SU(d1) generators. The framework is valid for composite systems of arbitrary dimension
d1×d2 and provides a direct computational route to the LQU from the spectral decomposition of the unperturbed state. We further specialize the theory to the quantum linear response regime, where the perturbation is generated by a time-dependent external field, and
w1 acquires explicit dependence on the driving frequency
ω, the eigenstates and occupation probabilities of the equilibrium Hamiltonian
H0, and the matrix elements of the coupling operator
A^. As an illustration, we apply the formalism to the isotropic Heisenberg model of two coupled spins driven by a local periodic magnetic field, obtaining closed-form expressions for the LQU as a function of temperature
T and frequency
ω. Comparison with the concurrence shows that above the entanglement critical temperature
Tc, the external field induces a resonantly enhanced quantum discord without generating entanglement, demonstrating that frequency acts as a tunable modulator of nonclassicality -- an effect of purely quantum-discord type inaccessible to entanglement-based quantifiers.
Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.
The study of Bell nonlocality and the bounds of quantum correlations, the so-called Tsirelson bounds, is fundamental to quantum information science and the exploration of the limits of quantum theory. While quantum bounds for qubit systems have been extensively characterized, determining tight quantum bounds for correlations attainable with high-dimensional quantum states and measurements remains a significant challenge. In this work, we propose a systematic derivation of bipartite Tsirelson and local bounds written in terms of sum-of-squares decompositions. Using this method, we discover novel bounds and recover established results for maximally entangled states of qubits and qu
dits.