Reprint of : Single-electron coherence: Finite temperature versus pure dephasing

We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in the presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electron states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electron states to the case of mixed states and clarifies the difference between different types of mixedness.     

Mixedness of the N-qubit states with exchange symmetry

The mixedness of the N-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix （RDM）, which can describe the mixedness, is completely determined by the expectation values 〈Sz〉 and 〈S±〉 for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa-Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case （J 〈 0）, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter △ 〉 △c.     

What dynamics can be expected for mixed states in two-slit experiments?

Weak-measurement-based experiments (Kocsis et al., 2011) have shown that, at least for pure states, the average evolution of independent photons in Young’s two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated assuming that the wave function associated with each particle is different, i.e., in the case of mixed (incoherent) states? This question is investigated here by means of two alternative numerical simulations of Young’s experiment, purposely devised to be easily implemented and tested in the laboratory. Contrary to what could be expected a priori, it is found that even for conditions of maximal mixedness or incoherence (total lack of interference fringes), experimental data will render a puzzling and challenging outcome: the average particle trajectories will still display features analogous to those for pure states, i.e., independently of how mixedness arises, the associated dynamics is influenced by both slits at the same time. Physically this simply means that weak measurements are not able to discriminate how mixedness arises in the experiment, since they only provide information about the averaged system dynamics.     

Factorization law for entanglement evolution of two qubits in non-Markovian pure dephasing channels

The entanglement evolution of two qubits in local, two-sided non-Markovian pure dephasing channels is investigated. It is found that for the two-sided pure dephasing channel case, when the qubits are initially prepared in a general class of states, whether pure or mixed, the entanglement can be expressed as the products of initial entanglement and the channels? action on the maximally entangled state. This provide us a good approximation to characterize the entanglement dynamics of arbitrary states to some extent.     

Comparison of dephasing times for vibrational and rotational coherent anti-Stokes Raman scattering: implications for velocimetry

Time-domain coherent anti-Stokes Raman scattering experiments have been carried out by probing vibrational and pure rotational lines of nitrogen in the Doppler broadened regime. The theoretical analysis of the transient responses outlines the role of the geometrical effects. For pure rotational CARS, it is shown that the main contribution to the dephasing of the Raman coherence results from the change in direction between the pump and anti-Stokes wave vectors whereas the difference between the modulus of these two wave vectors accounts for dephasing in vibrational CARS. Furthermore, we demonstrate that the range of operation of time-domain CARS velocimetry is extended by probing pure rotational lines. The predictions are validated by experiments which are performed both in a static gas cell and in a Mach 10 supersonic flow. Received: 30 March 2000 / Revised version: 9 June 2000 / Published online: 13 September 2000     

Dephasing effects in topological insulators

Topological insulators, a class of typical topological materials in both two dimensions and three dimensions,are insulating in bulk and metallic at surface. The spin-momentum locked surface states and peculiar transport properties exhibit promising potential applications on quantum devices, which generate extensive interest in the last decade. Dephasing is the process of the loss of phase coherence, which inevitably exists in a realistic sample. In this review, we focus on recent progress in dephasing effects on the topological insulators. In general, there are two types of dephasing processes: normal dephasing and spin dephasing. In two-dimensional topological insulators, the phenomenologically numerical investigation shows that the longitudinal resistance plateaus is robust against normal dephasing but fragile with spin dephasing. Several microscopic mechanisms of spin dephasing are then discussed. In three-dimensional topological insulators, the helical surface states exhibit a helical spin texture due to the spin-momentum locking mechanism. Thus, normal dephasing has close connection to spin dephasing in this case, and gives rise to anomalous “gap-like” feature. Dephasing effects on properties of helical surface states are investigated.     

Characteristic time and maximum mixedness: Single mode Gaussian states in dissipative channels

We derive an upper limit for the mixedness of single bosonic mode Gaussian states propagating in dissipative channels. It is a function of the initial squeezing and temperature of the channel only. Moreover the time at which von Neumann's entropy reaches its maximum value coincides with that of complete loss of coherence, thus defining a quantum-classical transition.     

The effect of stochastic dephasing on the entanglement and coherence of qutrits

By using negativity, we study the effect on the quantum entanglement of 2-qutrit states of stochastic dephasing which obeys the stationary Gauss-Markov process. The linear entropy used to measure coherence loss due to the stochastic dephasing is discussed. With analysis, we find that the time evolution of entanglement and the linear entropy depends not only on the structure of states of concern, but also on the strength of the fluctuations of the random variable in the stochastic process.     

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.     

有限维希尔伯特空间q-畸变谐振子偶相干态及其压缩和反聚束特性

从一般形式上构造了有限维希尔伯特（Ｈｉｌｂｅｒｔ）空间ｑ－畸变谐振子的偶相干态,并讨论了其量子统计特性。发现有限维希尔伯特空间的偶ｑ－相干态与通常无限维空间的偶ｑ－相干态或偶相干态有明显不同的压缩和反聚束特性。前者的偶ｑ－相干态不仅出现正交压缩,而且出现反聚束效应。     

类氢原子核质量对电子状态的影响

在孤立的两体复合系统中,讨论其中一体的变化如何影响另一体的状态,有助于了解单粒子混合态与纯态的关系.本文讨论5个孤立的一维类氢原子模型系统,原子核的质量互不相同.这5个两体(电子与原子核)复合系统的相对运动状态都处于纠缠态,其中电子状态都用约化密度矩阵表示的混合态描述.在原子核质量趋近无穷大的一维氢原子模型中,电子处于纯态.为比较这里的纯态和混合态,在位置表象中计算了这些混合态的纯度、它们分别与纯态的保真度、以及所有这些态的相干性.研究表明,原子核的质量越大,纯度和保真度越接近1,混合态的相干性与纯态的也越接近.这样的纯态及其相干性可以是这种混合态及其相干性的近似,并与原子核及库仑相互作用有关.     

偶奇相干态的q-类比

在偶奇相干态的基础上,构造出偶、奇q-相干态,并讨论了它们的光统计特性.计算分析表明:偶奇q-相干态的光统计特性,是完全不相同的.     

Catalytic Coherence Transformation and Distillation for Special Mixed States

The coherence transformation and distillation for a class of special mixed coherent states of rank-2 under incoherent operations (IO) is discussed. Similar to the entanglement transformation for mixed entangled states, the catalytic coherence transformation for this class of special mixed coherent states is analyzed. On the one hand, it is found that some of the mixed coherent states can be converted into other mixed coherent states under IO. But for those mixed coherent states which fail in the coherence conversion under IO, the catalytic coherence manipulation can solve this problem. In this case, a mixed coherent state cannot be converted into another under IO, while the coherence transformation can be realized with the help of coherence-assisted incoherent operations, that is, catalytic coherence transformation. On the other hand, these special mixed coherent states can be distilled into the maximally pure coherent states or mixed states of arbitrary dimensions by strictly incoherent operations with certain probabilities. Finally, the coherence transformation of this type of mixed states can be generalized to the case of higher rank in a similar way, which is discussed at the end of this paper.     

Disentanglement of 3-qubit states with stochastic dephasing

The effect of stochastic dephasing on the entanglement of 3-qubit states is analyzed. We find that the extent to which the entanglement vanishes depends not only on the strength of the stochastic dephasing, but also on the structure of states of concern under decoherence induced by the stochastic dephasing. The linear entropy used to measure coherence loss is evaluated.     

Change of decoherence scenario and appearance of localization due to reservoir anharmonicity

Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semiconductor quantum dots due to anharmonicity of phonon modes.     

在腔场与可移动镜子系统中对镜子位置的测量

描述利用腔场与镜的相互作用,对镜的位置坐标进行测量选域以使腔场变为Fock态的叠加态.并进一步讨论其压缩特性及相干性,通过数值计算,发现该腔场有非经典效应,即有一定的压缩效应和反聚束效应.     

基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

Noise dephasing in edge states of the integer quantum Hall regime

An electronic Mach-Zehnder interferometer is used in the integer quantum Hall regime at a filling factor 2 to study the dephasing of the interferences. This is found to be induced by the electrical noise existing in the edge states capacitively coupled to each other. Electrical shot noise created in one channel leads to phase randomization in the other, which destroys the interference pattern. These findings are extended to the dephasing induced by thermal noise instead of shot noise: it explains the underlying mechanism responsible for the finite temperature coherence time tau_{phi}(T) of the edge states at filling factor 2, measured in a recent experiment. Finally, we present here a theory of the dephasing based on Gaussian noise, which is found to be in excellent agreement with our experimental results.     

Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.     

Sufficient Conditions of the Same State Order Induced by Coherence

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l₁ norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d-dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.