Quantum correlations for two-qubit X states through the local quantum uncertainty

2017 ◽  
Vol 15 (03) ◽  
pp. 1750020 ◽  
Author(s):  
L. Jebli ◽  
B. Benzimoun ◽  
M. Daoud
Keyword(s):  
Quantum Correlations ◽  
Quantum Systems ◽  
Local Observable ◽  
Quantum Metrology ◽  
Quantum Uncertainty ◽  
Bipartite State ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Qubit States ◽  
Spin Coherent States

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.

Local quantum uncertainty and trace distance discord dynamics for two-qubit X states embedded in non-Markovian environment

2018 ◽  
Vol 32 (20) ◽  
pp. 1850218 ◽  
Author(s):  
Youssef Khedif ◽  
Mohammed Daoud
Keyword(s):  
Quantum Correlations ◽  
Trace Distance ◽  
Markovian Environment ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Limiting Case ◽  
Analytical Expressions ◽  
Qubit States ◽  
Markovian Regime

We investigate the behavior of quantum correlations in some specific Werner-like two-qubit states, where the qubit interacts individually with non-Markovian environment. We employ the local quantum uncertainty and trace distance discord to quantify the amount of quantum correlations between the evolved qubits and the corresponding analytical expressions are derived. For specific values of the parameters characterizing the whole system, the dynamics of quantum correlations exhibits collapse and revival phenomena. The influence of the non-Markovianity is also investigated to analyze the monotonic decay of quantum correlations in the limiting case of Markovian regime. Furthermore, we show that trace distance discord captures quantum correlations that cannot be revealed by local quantum uncertainty in some particular situations.

Local quantum uncertainty versus negativity through Gisin states

2021 ◽  
pp. 2150023
Author(s):  
A. Sbiri ◽  
M. Mansour ◽  
Y. Oulouda
Keyword(s):  
Sudden Change ◽  
Quantum Correlations ◽  
Mixed States ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Mixing Parameter ◽  
Local Quantum ◽  
Local Uncertainty ◽  
Bona Fide ◽  
Spin Coherent States

We investigate the pairwise quantum correlations in standard Gisin states and in Gisin states based on bipartite spin-coherent states by employing quantum negativity and quantum local uncertainty as bona fide quantum correlations measures. Gisin states are defined as mixtures of separable mixed states and some pure entangled ones. We compare the behavior of the two quantifiers of Gisin states and we find that both measures exhibit a sudden change in terms of the mixing parameter. Furthermore, we show that entangled Gisin states contain nonclassical correlations that are captured by the local quantum uncertainty and cannot be revealed by the negativity quantifier.

Local quantum uncertainty for a class of two-qubit X states and quantum correlations dynamics under decoherence

2017 ◽  
Vol 15 (01) ◽  
pp. 1750001 ◽  
Author(s):  
L. Jebli ◽  
B. Benzimoune ◽  
M. Daoud
Keyword(s):  
Quantum Discord ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Trace Distance ◽  
Von Neumann ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Two Parameters ◽  
Qubit States

A special emphasis is devoted to the concept of local quantum uncertainty as an indicator of quantum correlations. We study quantum discord for a class of two-qubit states parametrized by two parameters. Quantum discord based on local quantum uncertainty, von Neumann entropy and trace distance (Schatten 1-norm) are explicitly derived and compared. The behavior of quantum correlations, quantified via local quantum uncertainty, under decoherence effects is investigated. We show that the discordlike local quantum uncertainty exhibits the possibility of freezing behavior during its evolution.

scholarly journals Local quantum uncertainty as a robust metric to characterize discord-like quantum correlations in subsets of the chromophores in photosynthetic light-harvesting complexes

2020 ◽  
Vol 66 (4 Jul-Aug) ◽  
pp. 525
Author(s):  
M. Chávez-Huerta ◽  
F. Rojas
Keyword(s):  
Quantum Coherence ◽  
Light Harvesting ◽  
Green Sulfur Bacteria ◽  
Quantum Correlations ◽  
Light Harvesting Complexes ◽  
Thermal Equilibrium State ◽  
Light Harvesting Complex ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum

Green sulfur bacteria is a photosynthetic organism whose light-harvesting complex accommodates a pigment-protein complex called Fenna-Matthews-Olson (FMO). The FMO complex sustains quantum coherence and quantum correlations between the electronic states of spatially separated pigment molecules as energy moves with nearly a 100% quantum efficiency to the reaction center. We present a method based on the quantum uncertainty associated to local measurements to quantify discord-like quantum correlations between two subsystems where one is a qubit and the other is a qudit. We implement the method by calculating local quantum uncertainty (LQU), concurrence, and coherence between subsystems of pure and mixed states represented by the eigenstates and by the thermal equilibrium state determined by the FMO Hamiltonian. Three partitions of the seven chromophores network define the subsystems: one chromophore with six chromophores, pairs of chromophores, and one chromophore with two chromophores. Implementation of the LQU approach allows us to characterize quantum correlations that had not been studied before, identify the most quantum correlated subsets of chromophores, and determine that, in the strongest associations of chromophores, the LQU is a monotonically increasing function of the coherence.

The accelerated Gisin state: its non-locality, quantum correlations and efficiency to perform quantum masking

2021 ◽  
Vol 21 (15&16) ◽  
pp. 1274-1295
Author(s):  
A.G. Abdelwahab ◽  
A. Ghwail ◽  
N. Metwally ◽  
M.H. Mahran ◽  
A. -S. F. Obada
Keyword(s):  
Quantum Correlations ◽  
Local Behavior ◽  
Quantum Uncertainty ◽  
Acceleration Parameter ◽  
Masking Condition ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Non Local ◽  
Classical Correlations ◽  
Non Locality

The local and non local behavior of the accelerated Gisin state are investigated either before or after filtering process. It is shown that, the possibility of predicting the non-local behavior is forseen at large values of the weight of the Gisin and acceleration parameters. Due to the filtering process, the non-locality behavior of the Gisin state is predicted at small values of the weight parameter. The amount of non classical correlations are quantified by means of the local quantum uncertainty (LQU)and the concurrence, where the LQU is more sensitive to the non-locality than the concurrence. The phenomenon of the sudden changes is displayed for both quantifiers. Our results show that, the accelerated Gisin state could be used to mask information, where all the possible partitions of the masked state satisfy the masking criteria. Moreover, there is a set of states, which satisfy the masking condition, that is generated between each qubit and its masker qubit. For this set, the amount of the non-classical correlations increases as the acceleration parameter increases . Further, the filtering process improves these correlations, where their maximum bounds are much larger than those depicted for non-filtered states.

scholarly journals A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 263
Author(s):  
Paolo Gibilisco ◽  
Davide Girolami ◽  
Frank Hansen
Keyword(s):  
Quantum Correlations ◽  
Unified Approach ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Skew Information ◽  
Local Quantum ◽  
Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.

Examining quantum correlations in the XY spin chain by local quantum uncertainty

2015 ◽  
Vol 14 (4) ◽  
pp. 1429-1442 ◽  
Author(s):  
Jin-Liang Guo ◽  
Jin-Long Wei ◽  
Wan Qin ◽  
Qing-Xia Mu
Keyword(s):  
Spin Chain ◽  
Quantum Correlations ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Xy Spin Chain

Quantum interferometric power and the role of nonclassical correlations in quantum metrology for a special class of two-qubit states

2017 ◽  
Vol 31 (08) ◽  
pp. 1750052 ◽  
Author(s):  
H. El Hadfi ◽  
Y. Ait Taleb ◽  
M. Daoud
Keyword(s):  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Phase Estimation ◽  
Quantum Metrology ◽  
Von Neumann ◽  
Local Quantum ◽  
Parameter Precision ◽  
Qubit States

We analyze the effects of quantum correlations on the parameter precision in an interferometric configuration. As probe states, we consider a class of two-qubit states for which the analytical expression of the quantum interferometric power, quantifying the quantum correlations, is explicitly derived. Also, we give and analyze the local quantum Fisher information, which evaluates the sensitivity of the probe state to the phase shift, for some relevant local Hamiltonians. The discord-like quantum correlations based on the notion of quantum interferometric power are compared with the original quantum discord based on von Neumann entropy. We also examine the significance of quantum correlations in enhancing the precision of the phase estimation. Our study corroborates the recent series of investigations focusing on the role of quantum correlations other than entanglement on the efficiency of quantum metrology protocols.

scholarly journals Invariant entanglement and generation of quantum correlations under global dephasing

2018 ◽  
Vol 96 (7) ◽  
pp. 705-710 ◽  
Author(s):  
Göktuğ Karpat
Keyword(s):  
Quantum Entanglement ◽  
Dynamical Behavior ◽  
Sudden Change ◽  
Geometric Approach ◽  
Quantum Correlations ◽  
Systematic Analysis ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Time Invariant

We investigate the dynamics of quantum entanglement and more general quantum correlations quantified via negativity and local quantum uncertainty, respectively, for two-qubit systems undergoing Markovian collective dephasing. Focusing on a two-parameter family of initial two-qubit density matrices, we study the relation of the emergence of the curious phenomenon of time-invariant entanglement and the dynamical behavior of local quantum uncertainty. Developing an illustrative geometric approach, we demonstrate the existence of distinct regions of quantum entanglement for the considered initial states and identify the region that allows for completely frozen entanglement throughout the dynamics, accompanied by generation of local quantum uncertainty. Furthermore, we present a systematic analysis of different dynamical behaviors of local quantum uncertainty, such as its sudden change or smooth amplification, in relation with the dynamics of entanglement.

Sign in / Sign up

Export Citation Format

Share Document