Measurement-induced Disturbance Research Articles

Quantum Correlations in a Family of Bipartite Qubit-Qutrit Separable States

Quantum correlations in a family of bipartite separable qubit-qutrit quantum-classical correlated states are investigated by using two popular measures, i.e., the original quantum discord (OQD) method by Ollivier and Zurek [Phys. Rev. Lett. 88 (2001) 017901] and the measurement-induced disturbance (MID) method by Luo [Phys. Rev. A 77 (2008) 022301]. It is found that both of them are functions of a parameter partially characterizing the concerned states, however, quantum correlations evaluated via the convenient MID method are somewhat overestimated.

Analytic expressions of quantum correlations in qutrit Werner states

Quantum correlations in qutrit Werner states are extensively investigated with five popular methods, namely, original quantum discord (OQD) (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), ameliorated MID (AMID) (Girolami et al. in J Phys A Math Theor 44:352002, 2011), relative entropy (RE) (Modi et al. in Phys Rev Lett 104:080501, 2010) and geometric discord (GD) (Dakic et al. in Phys Rev Lett 105:190502, 2010). Two different analytic expressions of quantum correlations are derived. Quantum correlations captured by the former four methods are same and bigger than those obtained via the GD method. Nonetheless, they all qualitatively characterize quantum correlations in the concerned states. Moreover, as same as the qubit case, there exist quantum correlations in separable qutrit Werner states, too.

Dynamics of Measurement-Induced Disturbance for a Qubit-Qutrit System in Noninertial Frames

We investigate the dynamics of measurement-induced disturbance (MID) for a qubit-qutrit system in noninertial frames under various multi-local decoherence channels (i.e., dephasing, phase-flip, bit-(trit-) flip, bit-(trit-) phase-flip, and depolarizing channels). We find that, for any acceleration, the MID can decay in a monotonic way to zero or to a nonzero steady value (i.e., residual MID exists). Consequently, no sudden death of the MID occurs, which is different from entanglement.

Controllable quantum correlations of two-photon states generated using classically driven three-level atoms

We investigate the dynamics of two-photon correlations generated by the interaction of a three-level atom in the Ξ,Λ or V configuration, with two classical external driving fields, under the rotating-wave approximation, in the presence of level decays. Using the example of a rubidium atom in each configuration, with field strengths validating the single-photon approximation, we compute measurement-based correlations, such as measurement induced disturbance (MID), quantum discord (QD), and quantum work deficit (WD), and compare the results with that from quantum entanglement (concurrence). Certain correlation properties observed are generic, model independent and consistent with known results, e.g., MID is an upper bound on QD, QD and WD are monotonic, and the generic correlation behavior is strongly affected by the purity of the photon states. We observe that the qualitative hierarchy, monotonicity and steady-state behavior of the correlations can be controlled through the choice of parameters such as atomic decay constants and external driving field strengths. We point out how particular configurations are better suited to generating monotonic correlations in specific regimes and how the steady-state correlation behavior and hierarchy are affected by the population dynamics of the density matrix for different parameters. The possibility of using well studied quantum optical systems such as the three-level atom to generate, characterize and parametrically control mixed state quantum correlations establishes an important step in the direction of their implementation in quantum information tasks.

Analysis of the two-particle controlled interacting quantum walks

We have recently proposed the two-particle controlled interacting quantum walks for building quantum Hash schemes (Li et al. Quantum Inf Proc, 2012. doi: 10.1007/s11128-012-0421-8 ). In this paper, we adopt the mutual information, the measurement-induced disturbance and the quantum mutual information to measure the classical correlation, the quantum correlation and the total correlation between two particles respectively. Our conclusion is that the correlation between the particles of the two-particle controlled interacting quantum walks is similar to that of the two-particle interacting quantum walks. It is superb for keeping the quantum Hash scheme safe.

Measurement-induced disturbance and thermal negativity in 1D optical lattice chain

We study the measurement-induced disturbance (MID) in a 1D optical lattice chain with nonlinear coupling. Special attention is paid to the difference between the thermal entanglement and MID when considering the influences of the linear coupling constant, nonlinear coupling constant and external magnetic field. It is shown that MID is more robust than thermal entanglement against temperature T and external magnetic field B, and MID may reveal more properties about quantum correlations of the system, which can be seen from the point of view that MID can be nonzero when there is no thermal entanglement and MID can detect the critical point of quantum phase transition at finite temperature.

Influence of the phase damping for two-qubits system in the dispersive reservoir

An analytical solution of the master equation for two qubits-field system in the dispersive reservoir are investigated, the qubits are initially in werner states. Under the influence of the damping we investigate the quantum correlation in a two-qubit based on measurement-induced disturbance (MID). We compare MID and entanglement measured by negativity and illustrate their different characteristics. We find the effect of damping on MID is weaker than negativity. Negativity will experience a sudden transition but this will not happen for MID.

Quantum discord: ‘discord’ between the whole and its constituent

Quantum discord, a measure of quantum correlation beyond entanglement, is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information. In this paper, we report some new interpretations of discord which rely on the differences between measurement-induced effects on the local measured system and the whole system. Specifically, with proper quantitative definitions introduced in Buscemi et al (2008 Phys. Rev. Lett. 100 210504), we find that quantum discord can be interpreted as the differences of measurement-induced disturbance or information gain on the local measured system and on the whole system. Combined with previous similar results based on measurement-induced entanglement and decoherence, our results provide a unified view on quantum discord.

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems

We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin–Meshkov–Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser–Horne–Shimony–Holt–Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while, surprisingly, it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, the Clauser–Horne–Shimony–Holt–Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.

Death and revival of the quantum discord and the measurement-induced disturbance

Three different quantifiers, entanglement of formation (ENT), quantum discord (QD), and measurement-induced disturbance (MID), are used to measure the quantum correlations of two qubits in a common squeezed bath. A subspace was found for initial conditions in a squeezed bath, where the system experiences no decoherence. We relate the three measurements with the “distance” from the initial condition to the decoherence free subspace, in order to study the effect of the decoherence in the quantum correlations. We show examples of a system with quantum correlations even when entanglement is null. Furthermore, we study the necessary conditions for the system to become truly classical. We found that, under certain initial conditions and at specific times, the system becomes classical and both the QD and the MID vanish, thus observing the phenomena of sudden death and revival of the quantum correlations. Finally, we observe discontinuities in the QD.

A Classification of Correlations of Tripartite Mixed States

To obtain a classification of correlations of tripartite mixed states, various correlated states are introduced by using measurement-induced disturbance, including CCC, QC, GQC, CCX, CXC, XCC, CXX, XCX and XXC-states. Standard forms of them are established and equivalent characterizations of them are obtained in terms of normality and commutativity of the associated component operators.

Quantum correlation dynamics of two qubits in noisy environments: The factorization law and beyond

We investigate the quantum correlations of two qubits under conditions of single-sided and two-sided noisy channels when the initial state of the system belongs to a subclass of X structured ones in terms of measurement-induced nonlocality, measurement-induced disturbance and quantum discord. The results show that measurement-induced nonlocality has a factorization law, regardless of whether there are single-sided or two-sided noisy channels. However, there is no simple factorization relation for measurement-induced disturbance and quantum discord. Also, we compare the evolution of these quantum correlations as functions of time. For the four Bell initial states, we find that the measurement-induced disturbance evolution equations are the same when the channel is single-sided, but they will be divided into two categories when the channel is two-sided. Quantum correlations decay more quickly when the channel is two-sided. Furthermore, quantum discord presents sudden change in the derivative of its time evolution.

Quantum correlation of correlated two qubits interacting with a thermal field

The quantum correlation (QC) of two qubits coupled to a thermal field is investigated based on measurement-induced disturbance. It is found that QC does not exist only in the entangled state. Due to the thermal parameter, QC is inhibited from vanishing and the phenomenon of the death and birth of entanglement occurs. Due to the field-mode structure, QC is equal to zero for separated qubits, whereas for a maximally entangled state, it has a periodic asymptotic behavior which does not vanish. QC and entanglement differ when the qubit state is initially in the separated or entangled state.

Two quantum walkers sharing coins

We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random-walk characteristics, but we show that quantum walks with partial swapping of coins have complicated yet elegant interwalker correlations. Specifically we study the joint position distribution of the reduced two-walker state after tracing out the coins and analyze total, classical, and quantum correlations in terms of mutual information, quantum mutual information, and measurement-induced disturbance. Our analysis shows intriguing quantum features without classical analogs.

Measurement-induced disturbance and nonequilibrium thermal entanglement in a qutrit—qubit mixed spin XXZ model

We investigate the dynamics of nonequilibrium thermal quantum correlation of a qutrit-qubit mixed spin system coupled to two bosonic reservoirs at different temperatures using measurement-induced disturbance. The effects of initial states of the spins and temperatures of the reservoirs on measurement-induced disturbance and entanglement are discussed. The results demonstrate that measurement-induced disturbance is more robust than entanglement against the influence of both these factors and there is no sudden death phenomenon for measurement-induced disturbance. The dependences of steady-state measurement-induced disturbance and entanglement on coupling constant and anisotropy parameter are also studied. Steady-state entanglement vanishes for a ferromagnetic qutrit-qubit model, while steady-state measurement-induced disturbance exists for both the antiferromagnetic and ferromagnetic cases. Appropriately modulating the coupling constant and anisotropy parameter can strengthen quantum correlation.

Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states

The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here, we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation with discord, and characterize the maximally quantum-correlated mixed states, that simultaneously extremize both quantifiers at given von Neumann entropy: among all two-qubit states, these states possess the most robust quantum correlations against noise.

Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord

Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate non-classicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly the trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of non-classicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.

Quantum correlations in spin models

Bell nonlocality, entanglement and nonclassical correlations are different aspects of quantum correlations for a given state. There are many methods to measure nonclassical correlations. In this paper, nonclassical correlations in two-qubit spin models are measured by the use of measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A 77 (2008) 022301] and geometric measure of quantum discord (GQD) [B. Dakić, V. Vedral, C. Brukner, Phys. Rev. Lett. 105 (2010) 190502]. Their dependences on external magnetic field, spin–spin coupling, and the Dzyaloshinskii–Moriya (DM) interaction are presented in detail. We also compare Bell nonlocality, entanglement measured by concurrence, MID and GQD and illustrate their different characteristics.

Measurement-induced disturbances and nonclassical correlations of Gaussian states

We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous-variable systems by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states comprising pure states where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two-mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states.

Measurement-induced disturbance and thermal negativity of qutrit–qubit mixed spin chain

We investigate the quantum correlation in a qutrit–qubit mixed spin chain based on measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A, 77 (2008) 022301]. We also compare MID and thermal entanglement measured by negativity and illustrate their different characteristics.