Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels

2015

Mod. Phys. Lett. B

Using the quantum renormalization group (QRG) method, we investigate the ground state geometric measure of quantum discord (GQD) of the transverse Ising model. The analytical expression of GQD together with the RG recurrence relations are obtained. The critical and scaling behaviors of GQD are investigated. Our results show that with the increasing of RG steps, GQD (first derivative of GQD) exhibits sudden change (dip) in behavior at the critical point, which indicates that the system undergoes phase transitions between the Ising and the paramagnetic phases. The critical exponent that governs the divergences of the first derivative of GQD is calculated. How the critical point of the model is approached as the increasing of the system size is revealed.

“…the GQD of the zero RG step Consequently, the GQD of each RG steps can be calculated by combining Eqs. (16) and (20). For the nth RG step, the GQD can be calculated by…”

Section: Calculation Of the Ground State Geometric Quantum Discordmentioning

confidence: 96%

“…Following their definition, many works concerned with GQD have been reported. [16][17][18][19][20] Shan et al 19 proved that the topological phase transition can be captured by the GQD. Fan et al 20 investigated the GQD in frustrated Heisenberg chain.…”

Section: Introductionmentioning

confidence: 99%

The renormalization of geometric quantum discord in the transverse Ising model

2015

Mod. Phys. Lett. B

“…However, the quantum discord does not have an analytic or operational expression in general, because of the supreme in its original definition [3,4]. In this work, we adopt the definition of GMQD [13,14] as its amount, and calculate it for the case with equal a priori overlaps. For our bipartite p-4 system in the space H S ⊗ H A with dim H S = 3 and dim H A = 2, the state (2) can be represented as…”

Section: Lf Xu Et Almentioning

confidence: 99%

Assisted optimal state discrimination without entanglement

Liang

et al. 2014

EPL

PACS 03.65.Ta -Foundations of quantum mechanics; measurement theory PACS 03.67.Mn -Entanglement measures, witnesses, and other characterizations PACS 42.50.Dv -Quantum state engineering and measurements Abstract -A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of d states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a priori probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.Introduction. -Quantum correlations contained in composite quantum states play important roles in quantum information processing and have been widely studied from various perspectives. Many concepts have been presented to reflect these correlations, such as quantum entanglement [1], Bell nonlocality [2], and quantum discord [3,4]. Entanglement had been regarded as the only resource for demonstrating the superiority of quantum information processing [1,5]. However, recent studies [6,7] show that the algorithm for deterministic quantum computation with one qubit (DQC1) can surpass the performance of the corresponding classical algorithm in the absence of entanglement between the control qubit and a completely mixed state. The quantum discord, which measures the nonclassical correlations and can exist in a separable state, is regarded to be the key resource in this quantum algorithm and has gained wide attention in recent years. Based on a unified view [8] of quantum and classical correlations, another type of quantum correlations called dissonance was put forward. Quantum dissonance measures the nonclassical correlations with entanglement being completely excluded. For a separable state, its dissonance is exactly

“…Moreover, from then on, people gradually began to pay close attention to the new kind of QC, i.e., QCBEs. Several years later, a number of works [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ] about QCBEs emerged, including its recognition and applications. Consequently, recently, QCBE study has formed a hot field in quantum information and computation, and many methods have been proposed or developed to investigate QCBEs in various quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Increasing Quantum Correlations Based on Measurement-Induced Disturbance via a Swapping Procedure with Two-Qubit Mixed States

Xie

et al. 2021

Entropy

In this paper, quantum correlation (QC) swapping for certain separable two-qubit mixed states is treated. A QC quantifier, measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), is employed to characterize and quantify QCs in the relevant states. Properties of all QCs in the swapping process are revealed. Particularly, it is found that MID can be increased through QC swapping for certain separable two-qubit mixed states.