Relative Entropy Of Coherence Research Articles

Enhancing quantum coherence in multiqubit-interacting system

Abstract We propose a quantum coherence protection scheme for a two-qubit system by considering the exact evolution of multi-interacting qubits in a common reservoir. We find that the l 1 norm of coherence and the relative entropy of coherence can be noticeably enhanced by increasing the number of qubits in the weak/strong system-environment coupling regime, which contrasts sharply with the impact of coupling between qubits. Moreover, in the infinite-time limit, all the coherence measures reach their steady values which are determined only by the number of qubits.

Quantum coherence and Rényi mutual information in Heisenberg XYZ system under non-uniform field

We investigate the thermal and magnetic quantum coherence in the Heisenberg XYZ system. To accomplish this, we employ three measures: the L1 norm coherence, the relative entropy coherence, and the Rényi mutual information (RMI). By performing these measures, we can accurately describe the quantum behaviors of the Heisenberg XYZ system. During the process of characterization, we have found both similarities and distinctive properties. Under a non-uniform field, the magnetic field can enhance the RMI for different coefficients α. All of the analytical and numerical results are described in details.

Detecting quantum phase localization using Arnold tongue

The dynamical phase localization of a single qubit in a dissipative bath is investigated. We show that phase preference persists in the long time limit only for a non-Markovian evolution with a finite detuning implying that non-Markovianity is required for phase localization. The maximum of the shifted phase distribution exhibits an Arnold tongue like feature where the phase localized and phase delocalized regions are distinctly separated. We show the formation of Arnold tongue using the relative entropy of coherence as well. From our work we propose that Arnold tongue can be used to detect dynamical phase localization even when there is no synchronization present in the system.

Effects of intrinsic decoherence on quantum coherence and correlations between spins within a two-dimensional honeycomb lattice graphene layer system

This research delves into the influence of intrinsic decoherence on the behavior of quantum correlations and coherence between two interacting qubits in a graphene-based system. To evaluate the amount of nonclassical correlations in the system, we employ local quantum uncertainty (LQU), and to assess quantum coherence we use the relative entropy of coherence [Formula: see text] and [Formula: see text]-norm [Formula: see text]. We assume that the system is initially prepared in an extended-Werner-like (EWL) state, and we investigate how these quantifiers evolve over time and examine their sensitivity to various graphene layer system parameters, mixture parameter of the initial state and the intrinsic decoherence rate. Our results indicate that by adjusting the wave number operators, decreasing the intrinsic decoherence rate, and increasing the initial state mixing parameter, it is possible to enhance both quantum correlations and coherence within the two-dimensional honeycomb lattice system. In addition, we found that quantum coherence is more resilient to intrinsic decoherence than LQU, moreover, the [Formula: see text]-norm is more robust than the relative entropy of coherence.

Depiction of an external classical field effects on a four-level W-configuration atom embedded in a coherent cavity field

This paper examines the dynamics of a W-configuration four-level atom in a quantized cavity field and the system driven by an external classical field. By applying some canonical transformations, we derive analytical solutions to the Schrödinger equation for the corresponding Hamiltonian. We have analyzed the impact of the external field and detuning parameters on the system’s relative entropy of coherence, Wigner function, and Pancharatnam phase. Our findings suggest that the external field parameter greatly affects the coherence of the system, whereas the detuning parameters may increase its maximum bounds. Furthermore, we have utilized the Wigner function as a tool to measure the quantumness and classicality of the system in its phase space. Our results indicate that the external field has a greater impact on the classicality of the system than the detuning parameters. Additionally, we have observed rapid oscillations in the dynamics of the Pancharatnam phase for large detuning values. It is worth noting that the external field reduces the number of phase jumps in the system.

Complementarity between quantum coherence and mixedness: a majorization approach

Quantum coherence is a relevant resource for various quantum information processing tasks, but it is fragile since it is generally affected by environmental noise. This is reflected in the loss of purity of the system, which in turn limits the amount of quantum coherence of it. As a consequence, a complementarity relation between coherence and mixedness arises. Previous works characterize this complementarity through inequalities between the ℓ 1-norm of coherence and linear entropy, and between the relative entropy of coherence and von Neumann entropy. However, coherence–mixedness complementarity is expected to be a general feature of quantum systems, regardless of the measures used. Here, an alternative approach to coherence–mixedness complementarity, based on majorization theory, is proposed. Vectorial quantifiers of coherence and mixedness, namely the coherence vector and the spectrum, respectively, are used, instead of scalar measures. A majorization relation for the tensor product of both vectorial quantifiers is obtained, capturing general aspects of the trade-off between coherence and mixedness. The optimal bound for qubit systems and numerical bounds for qutrit systems are analyzed. Finally, coherence–mixedness complementarity relations are derived for a family of symmetric, concave and additive functions. These results provide a deeper insight into the relation between quantum coherence and mixedness.

Coherence as entropy increment for Tsallis and Rényi entropies

Relative entropy of coherence can be written as an entropy difference of the original state and the incoherent state closest to it when measured by relative entropy. The natural question is, if we generalize this situation to Tsallis or Rényi entropies, would it define good coherence measures? In other words, we define a difference between Tsallis entropies of the original state and the incoherent state closest to it when measured by Tsallis relative entropy. Taking Rényi entropy instead of the Tsallis entropy, leads to the well-known distance-based Rényi coherence, which means this expression defined a good coherence measure. Interestingly, we show that Tsallis entropy does not generate even a genuine coherence monotone, unless it is under a very restrictive class of operations. Additionally, we provide continuity estimate for Rényi coherence. Furthermore, we present two coherence measures based on the closest incoherent state when measures by Tsallis or Rényi relative entropy.

Degeneration of the Grover search algorithm with depolarization in the oracle-box wires

Grover’s search algorithm and similar techniques are widely used in quantum information science. Communication lines with the so-called oracle are one of inevitable vulnerabilities of quantum search. The impact of localized dephasing and amplitude damping on Grover’s algorithm had already been discussed in recent literature. In this paper, we study the influence of depolarization in the oracle-box wires on the search process. It is shown that even low level of noise is sufficient to degenerate Grover’s algorithm. Complementarity relations between the relative entropy of coherence and the success probability in the presence of depolarization are studied as well.

Beam splitter as quantum coherence-maker

The aim of this work is to answer the question of how much quantum coherence a beam splitter is able to produce. To this end, we consider as the variables under study both the amount of coherence of the input states as well as the beam splitter characteristics. We conclude that there is an optimal combination of these factors making the gain of coherence maximum. In addition, the two-mode squeezed vacuum arises as the studied state most capable of gaining coherence when passing through a beam splitter. These results are qualitatively equivalent for the l1-norm of coherence and the relative entropy of coherence.

Trade-off relations of quantum resource theory in neutrino oscillations

The violation of the classical bounds imposed by Leggett-Garg inequalities has tested the quantumness of neutrino oscillations (NOs) over a long distance during the propagation. The measure of quantumness in experimentally observed NOs is studied via quantum resource theory (QRT). Here, we focus on the trade-off relations of QRT in the three-flavor NOs, based on Bell-type violations, first-order coherence and intrinsic concurrence, and the relative entropy of coherence. For the electron and muon antineutrino oscillations, the analytical trade-off relations obeyed by the Bell-CHSH inequality of pairwise flavor states in this three-flavor neutrino system are obtained; the sum of the maximal violation of the CHSH tests for three pairwise flavor states is less than or equal to 12. Moreover, there exists an equality relation concerning first-order coherence and intrinsic concurrence in NOs, showing how much quantum resources flow between first-order coherence and intrinsic concurrence during the neutrino propagation. In addition, it is found that the tripartite coherence of three-flavor system is equal to or larger than the sum of the coherence of reduced bipartite flavor states. The trade-off relations of QRT provide a method for studying how the quantum resources convert and distribute in NOs, which might inspire the future applications in quantum information processing using neutrinos.

Quantifying coherence relative to channels via metric-adjusted skew information

In terms of the metric-adjusted skew information (an important and versatile class of quantum Fisher information), which generalizes the seminal Wigner-Yanase skew information arising naturally from the study of quantum measurement, we propose a family of coherence measures of states relative to quantum channels, and reveal their basic properties such as unitary covariance, convexity, and monotonicity. Furthermore, we evaluate these coherence measures of states relative to several prototypical quantum channels, and make a comparative study for this family of coherence measures with relative entropy of coherence. This provides a general approach to coherence of states relative to quantum channels, which also captures decoherence on the states caused by quantum channels and asymmetry of states relative to quantum channels.

Enhancing the information of nonlinear SU(1, 1) quantum systems interacting with a two-level atom

The effect of nonlinearity, initial atomic state, and different resonance cases on the interaction between nonlinear SU (1, 1) quantum states and a two-level atom is discussed. The optimal behaviours of decoherence, entanglement and quantum coherence are predicted via using the skew information, tomographic entropy, and the relative entropy of coherence, respectively. It is shown that the detuning parameter has a destructive effect on the coherence and consequently on the entanglement if the quantum system is regulated in the ideal SU (1, 1) quantum systems. For the nonlinear SU (1, 1) quantum systems, the ability to suppress the decay of entanglement induced by the detuning may be increased by preparing the initial atomic state in its excited state.

Encoding Classical Information Into Quantum Resources

We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is the twirling channel over some unitary group, we find matching one-shot lower bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.

Quantumness of Pure-State Ensembles via Coherence of Gram Matrix Based on Generalized α-z-Relative Rényi Entropy

The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state ensemble can thus be quantified by the coherence of the Gram matrix [Europhys. Lett. \textbf{134} 30003]. Instead of the $l_1$-norm of coherence and the relative entropy of coherence, we utilize the generalized $\alpha$-$z$-relative R\'enyi entropy of coherence of the Gram matrix to quantify the quantumness of a pure-state ensemble and explore its properties. We show the usefulness of this quantifier by calculating the quantumness of six important pure-state ensembles. Furthermore, we compare our quantumness with other existing ones and show their features as well as orderings.

Coherence resource power of isocoherent states.

We address the problem of comparing quantum states with the same amount of coherence in terms of their coherence resource power given by the preorder of incoherent operations. For any coherence measure, two states with null or maximum value of coherence are equivalent with respect to that preorder. This is no longer true for intermediate values of coherence when pure states of quantum systems with dimension greater than two are considered. In particular, we show that, for any value of coherence (except the extreme values, zero and the maximum), there are infinite incomparable pure states with that value of coherence. These results are not peculiarities of a given coherence measure, but common properties of every well-behaved coherence measure. Furthermore, we show that for qubit mixed states there exist coherence measures, such as the relative entropy of coherence, that admit incomparable isocoherent states.

Experimental Investigation of Quantum Uncertainty Relations With Classical Shadows

The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, l1 norm of coherence, and coherence of formation. Instead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all-optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate that the tightness of quantum coherence lower bounds depends on the reference bases and the purity of the quantum state.

Quantum coherence bounds the distributed discords

Establishing quantum correlations between two remote parties by sending an information carrier is an essential step of many protocols in quantum information processing. We obtain trade-off relations between discords and coherence within a bipartite system. Then we study the distribution of coherence in a bipartite quantum state by using the relations of relative entropy and mutual information. We show that the increase of the relative entropy of discord between two remote parties is bounded by the nonclassical correlations quantified by the relative entropy of coherence between the carrier and two remote parties, providing an optimal protocol for discord distribution and showing that quantum correlations are the essential resource for such tasks.

Dynamics of quantum Fisher information and quantum coherence of two interacting atoms under time–fractional analysis

In this paper, we give an exact general solution to the fractional Schrödinger equation of two interacting atoms. It consists of using the Riemann–Liouville fractional integral operator to examine the interaction between two identical atoms under temporal–fractional evolution. The dynamics of quantum Fisher information with respect to changes in the phase parameter and the quantum coherence by means of the l 1 -norm and relative entropy of coherence are discussed. Moreover, the analytical fractional solution allows us to evaluate the relationship between the estimation precision of the phase parameter and the coherence measures for various atom–atom states. Indeed, the obtained results show a good similarity between these measures for certain critical values of the phase parameter. In addition, it is observed that initially, for such coherent-like fractional states, the amount of quantum Fisher information may be sensitive or insensitive to changes in the phase parameter. Therefore, one can conclude that quantum Fisher information can be considered as an indicator of quantum coherence in a composite quantum state.

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

We investigate quantum phase transitions for q-state quantum Potts models (q = 2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen–Shannon divergence, the relative entropy of coherence, and the l1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.

Estimating coherence with respect to general quantum measurements

The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., to a von Neumann measurement. Recently, generalized quantum coherence with respect to general positive operator-valued measurements has been presented. Several well-defined coherence measures, such as the relative entropy of coherence \(C_{r}\), the \(l_{1}\) norm of coherence \(C_{l_{1}}\) and the coherence \(C_{T,\alpha }\) based on Tsallis relative entropy with respect to general POVMs have been obtained. In this work, we investigate the properties of \(C_{r}\), \(C_{l_{1}}\) and \(C_{T,\alpha }\). We estimate the upper bounds of \(C_{l_{1}}\); we show that the minimal error probability of the least square measurement state discrimination is given by \(C_{T,1/2}\); we derive the uncertainty relations given by \(C_{r}\), and calculate the average values of \(C_{r}\), \(C_{T,\alpha }\) and \(C_{l_{1}}\) over random pure quantum states. All these results include the corresponding results of the conventional coherence as special cases.