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Register a new userOne-way quantum deficit and quantum coherence in the anisotropic $XY$ chain
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In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the $XY$ spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at $lambda=1$. When $lambdale1$, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an $XX$ model and an Ising chain at the finite temperatures.
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Originating in questions regarding work extraction from quantum systems coupled to a heat bath, quantum deficit, a kind of quantum correlations besides entanglement and quantum discord, links quantum thermodynamics with quantum correlations. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the $XY$ model and its extend model: the extended Ising model. We find that the one-way deficit susceptibility is able to characterize the quantum phase transitions in the $XY$ model and even the topological phase transitions in the extend Ising model. This study may enlighten extensive studies of quantum phase transitions from the perspective of quantum information processing and quantum computation, including finite-temperature phase transitions, topological phase transitions and dynamical phase transitions of a variety of quantum many-body systems.
The one-way quantum deficit, a measure of quantum correlation, can exhibit for X quantum states the regions (subdomains) with the phases $Delta_0$ and $Delta_{pi/2}$ which are characterized by constant (i.e., universal) optimal measurement angles, correspondingly, zero and $pi/2$ with respect to the $z$-axis and a third phase $Delta_vartheta$ with the variable (state-dependent) optimal measurement angle $vartheta$. We build the complete phase diagram of one-way quantum deficit for the XXZ subclass of symmetric X states. In contrast to the quantum discord where the region for the phase with variable optimal measurement angle is very tiny (more exactly, it is a very thin layer), the similar region $Delta_vartheta$ is large and achieves the sizes comparable to those of regions $Delta_0$ and $Delta_{pi/2}$. This instils hope to detect the mysterious fraction of quantum correlation with the variable optimal measurement angle experimentally.
A method for calculating the one-way quantum deficit is developed. It involves a careful study of post-measured entropy shapes. We discovered that in some regions of X-state space the post-measured entropy $tilde S$ as a function of measurement angle $thetain[0,pi/2]$ exhibits a bimodal behavior inside the open interval $(0,pi/2)$, i.e., it has two interior extrema: one minimum and one maximum. Furthermore, cases are found when the interior minimum of such a bimodal function $tilde S(theta)$ is less than that one at the endpoint $theta=0$ or $pi/2$. This leads to the formation of a boundary between the phases of one-way quantum deficit via {em finite} jumps of optimal measured angle from the endpoint to the interior minimum. Phase diagram is built up for a two-parameter family of X states. The subregions with variable optimal measured angle are around 1$%$ of the total region, with their relative linear sizes achieving $17.5%$, and the fidelity between the states of those subregions can be reduced to $F=0.968$. In addition, a correction to the one-way deficit due to the interior minimum can achieve $2.3%$. Such conditions are favorable to detect the subregions with variable optimal measured angle of one-way quantum deficit in an experiment.
The spin-1/2 XXZ chain in a uniform magnetic field at thermal equilibrium is considered. For this model, we give a complete classification of all qualitatively different phase diagrams for the one-way quantum work (information) deficit. The diagrams can contain regions (phases, fractions) with both stationary and variable (state-dependent) angles of optimal measurement. We found cases of phase diagrams in which the sizes of regions with the variable optimal measurement angle are large and perhaps such regions can be detected experimentally. We also established a relationship between the behavior of optimal measurement angles near the boundaries separated different regions and Landaus theory of phase transitions of the second and first kind.
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and coherence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible for quantum interference in the system. Here we will use coherence measure to quantify the interference in the discrete-time quantum walk. We show coherence in the position and coin space, together and independently, and present the contribution of coherence to the quantum interference in the system. This study helps us to differentiate the localization seen in one dimensional discrete-time quantum walks due to different forms of disorders and topological effects.
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