L1 Norm Of Coherence Research Articles

Quantum Chaos and Coherence: Random Parametric Quantum Channels

The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding l1-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.

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.

Entanglement of a cavity with a three-level atom and a graphene membrane in the presence of a laser field

This paper examines the entanglement and coherence of a hybrid quantum system in the presence of an external laser field. The hybrid system is composed of a single-mode cavity field containing a vibrating graphene membrane and a superconducting qutrit in a cascade configuration. Specifically, we investigate how the coupling of qutrit-graphene, detuning parameters, and external field coupling affects different measures, such as negativity tangle, algebraic tangle, geometric tangle, and the l1 norm of coherence. Our results demonstrate that the upper bounds of tangle measures and coherence decrease with increasing the detuning parameters. The external field amplifies the detrimental impact caused by detuning. Furthermore, heightened qutrit-graphene coupling elevates the maximum bounds of tangle and coherence quantifiers, while also increasing the frequency of oscillations.

Dynamics of an atomic system associated with a cavity-optomechanical system

This paper introduces the effective Hamiltonian of two two-level atoms inside a cavity with a movable mirror. The temporal evolution of the output density state that includes the interaction between movable mirror, atoms, and field is obtained. The dynamical properties of the quantum correlations of the system are studied via l1-norm of coherence, Entanglement of Formation (EoF) and Bell non-locality. The results shown that the phenomena of coherence, and non-locality are approached to the degree of entanglement as the initial atomic state is set in an excited state. However, different chaotic behavior is generated for the coherence at the initially mixed state. Overall, the temporal evolution of entanglement is an intermediate correlation that lies in between coherence and normalized Bell non-locality.

Influence of an External Classical Field on a ♢ Four-Level Atom Inside a Quantized Field

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dressed states, the exact solution of the Schrödinger equation is obtained. The occupation of atomic levels and statistical population inversion is studied. Our results show that the classical field parameter dissolved the collapse periods and increased the maximum bounds of the upper state, while decreasing the lower bounds of the lower state. The detuning parameters reduce the minimum bounds of atomic levels and their inversion. On the other hand, the linear entropy and l1 norm of coherence are employed to measure the temporal evolution of the mixedness and coherence. It is found that the driven classical field improves the temporal evolution of the mixedness and lower bounds of coherence. However, the detuning parameters have a destructive effect on the mixedness and lower bounds of coherence. The intensity of the external classical field is regarded as a control parameter with different values of detuning parameters.

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.

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.

Quantum Coherence of Qubit States with respect to Mutually Unbiased Bases

We study the coherence of qubit states with respect to any set of mutually unbiased bases (MUBs), in terms of the l1 norm of coherence, the modified trace norm of coherence and the geometry measure of coherence. We present the arbitrary expressions of a complete set of MUBs in C2 and the forms of any qubit states under these complete sets of MUBs. Then we calculate coherence of qubit states with respect to any complete sets of MUBs based on different coherence measures. It is shown that the sum of the coherence or the squared coherence is upper or lower bounded. We derive analytically these bounds and establish tight relations between quantum coherence and mutually unbiased bases.

Geometry of skew information-based quantum coherence

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases (MUBs). We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs. Moreover, we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels. The results show similar as well as different features compared with relative entropy of coherence and l1 norm of coherence.

Renormalization of quantum coherence and quantum phase transition in the Ising model

Quantifying quantum coherence of a given system not only plays an important role in quantum information science but also promotes our understanding of some basic problems, such as quantum phase transition. Conventional quantum coherence measures, such as l1-norm of coherence and relative entropy of coherence, are widely used to study quantum phase transition. Here we adopt a basis-independent coherence measure that is a quantum version of the Jensen–Shannon divergence to investigate the property of total quantum coherence, as well as its two contributions in quantum critical systems. Based on the quantum renormalization group method, we propose an analysis of the distribution of quantum coherence in the Ising system near the quantum critical point. We directly obtain the tradeoff relation, singular property, and scaling behavior in the Ising system. Furthermore, the monogamy relation is also studied in detail. These results further expand our understanding of quantum coherence as well as to enlarge the applications in using quantum coherence to reflect quantum critical phenomena.

The n-th Decay Rate of Coherence for Bell-diagonal States Under Quantum Channels

We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the n-th decay rate and investigate the coherence of Bell-diagonal states under n iterations of channels. We derive explicit formulas of the n-th decay rates based on l1 norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger n is, the faster the n-th decay rate decreases as the parameter p of Bell-diagonal states increases. Moreover, for any fixed n, with the increase of p, Bell-diagonal states can be completely incoherent under generalized amplitude damping (GAD) channels, depolarization (DEP) channels and phase flip (PF) channels, while this is not the case for bit flip (BF) channels and bit-phase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew information-based coherence of Bell-diagonal states under different channels when the n-th decay rate is one, i.e., the coherence is frozen. It is shown that compared with BF and BPF channels, when n is large enough, the coherence of Bell-diagonal states will not be frozen under GAD, DEP and PF channels. For skew information-based coherence, similar properties of coherence freezing are found.

Decoherence and visibility enhancement in multipath interference

We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease, but under certain conditions, to an increase of the fringe contrast. Here we explain this seemingly counter-intuitive effect based on a model for a multi-path interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multi-path situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the l1 norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multi-path interference, and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.

Coherence of Superposition States**Supported by the National Natural Science Foundation of China under Grant Nos. 61671280, 11771009, and 11847101; by the Natural Science Basic Research Plan in Shaanxi Province of China under Grant No. 2017KJXX-92; by the Fundamental Research Funds for the Central Universities under Grant No. GK201902007 and by the Funded Projects for the Academic Leaders and Academic Backbones,

We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with l1-norm of coherence. Our upper bound is tighter than the one presented by Liu, et al. [Quantum Inf. Process. 15 (2016) 4209.] We also generalize the results to the case that the superposition is constituted with more than two states in high dimension, and we give the corresponding upper bounds.

Tighter Superadditivity Relations in Multiqubit Systems

Superadditivity relations characterize the distributions of coherence in multipartite quantum systems. In this work, we investigate superadditivity relations related to the l1 norm of coherence $$\mathcal {C}_{l_{1}}$$ . Superadditivity relations for the αth power of $$\mathcal {C}_{l_{1}}$$ have also been derived, which are gradually tighter for every multiqubit states.

Operational Interpretations of the l1 Norm Coherence in Pure Quantum Systems

The operational property of quantum coherence plays an important role in the development of the coherent resource theory. As one of the qualified measures of coherence, the l1 norm of coherence is easily computable, but it is difficult to find an intuitionistic interpretation. In this paper, we provide operational interpretations of the l1 norm of coherence as coherence distillation and discriminating subchannels separately. From the view of coherence distillation, the l1 norm of coherence is directly related to the maximum distance between the given state and the maximally coherent state under some incoherent operation, so it can be reviewed as the distillation of coherence from the given state. In the aspect of the subchannel discrimination, the l1 norm of coherence can characterize the advantage of coherent states in subchannel discrimination, because any coherent state provide a higher probability of successful discriminating subchannels than that of all incoherent states.

Variance Measure of Coherence of Quantum Pure States

We provide an expression for the measure of coherence of quantum pure states, which is obtained by quantifying the deviation or distance between the measured state and the maximally coherent states in the same Hilbert space. We classify quantum pure states in a Hilbert space according to their coherence and prove that the variance measure of coherence is proper for all quantum pure states. We demonstrate that the variance measure of coherence is simpler and easier to obtain than the l1-norm of coherence and the relative entropy of coherence.

Nonlocal advantage of quantum coherence in the Heisenberg XY model

Quantum correlations in a state can be quantified from different aspects. The nonlocal advantage of quantum coherence (NAQC) captures quantum correlation stronger than entanglement and Bell nonlocality. We investigate the NAQC-type quantum correlation in the Heisenberg XY model and showed that both the anisotropy of the interaction between two spins and the external transverse magnetic field can serve as efficient parameters for tuning the NAQC-type quantum correlation. In particular, for the relative low temperature case there is a finite parameter region in which the strength of the NAQC-type quantum correlation is of about its maximum 1. We also found there are quantum states for which the NAQC-type quantum correlations defined by the l1 norm of coherence and the relative entropy of coherence have a different ordering.

Decay Rate of the l1 Norm Coherence in Single-Qubit Systems

We examine to what extent the l1 norm of coherence through an open quantum system is affected by noise. To discuss the effect of the noise, we give a definition of the decay rate of the l1 norm of coherence, i.e., the value of the coherence of initial states divided by the coherence of final states. Then we use the measure of the decay of coherence to discuss to what extent several noisy channels affects the coherence. We find that the decay rate is independent of the initial state parameters but only related to parameters of the phase flip channels, the depolarizing channels, and the amplitude channels. However, the decay rate is related to the initial state parameters and parameters of the bit flip channels. Contrary to the view at first glance, we find that the bit flip channels even have cohering power.

Enhancing two-qubit quantum coherence in a correlated dephasing channel

We investigate how the classical correlations between successive actions of a colored dephasing channel affect the decoherence of a two-qubit system. Our calculation shows that the l1 norm of coherence, the relative entropy of coherence, and the robustness of coherence can be noticeably enhanced by increasing the strength of classical correlations in the whole time interval during which the two qubits pass through the channel, while the coherence weight is enhanced only when exceeds a critical value. Moreover, in the infinite-time limit, all the coherence measures reach their steady values which are determined only by .

Geometric coherence and quantum state discrimination

The operational meaning of coherence measure lies at the very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von Neumann measurement. On the other hand, we also show that a task to ambiguously discriminate a set of linearly independent pure states can be regarded as a problem of calculating geometric coherence. That is, we reveal an equivalence relation between ambiguous quantum state discrimination and geometric coherence. Based on this equivalence, moreover, we improve the upper bound for geometric coherence and give the explicit expression of geometric coherence for a class of states. Besides, we establish a complementarity relation of geometric coherence and path distinguishability, with which the relationship between l1-norm of coherence and geometric coherence is obtained. Finally, with geometric coherence, we study multiple copies of quantum state discrimination and give an example to show how to discriminate two pure states.