Product-form monogamy relations of entanglement in multiqubit systems

2021 ◽  
pp. 2150022
Author(s):  
Jia-Bin Zhang ◽  
Tao Li ◽  
Zhi-Xi Wang
Keyword(s):  
Lower Bound ◽  
Quantum Entanglement ◽  
Quantum Systems ◽  
Product Form ◽  
Multipartite Entanglement ◽  
Multi Body ◽  
Monogamy Relations

Monogamy relations of entanglement play an important role in quantum systems, however, most of them are given in summation form. In this paper, we investigate the product-form monogamy relations of multipartite entanglement in terms of the [Formula: see text]th power of concurrence and negativity. Compared with the existing monogamy relations, the product-form monogamy relations of multi-body quantum entanglement have a stricter lower bound.

scholarly journals Heuristic for estimation of multiqubit genuine multipartite entanglement

2015 ◽  
Vol 13 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Paulo E. M. F. Mendonça ◽  
Marcelo A. Marchiolli ◽  
Gerard J. Milburn
Keyword(s):  
Lower Bound ◽  
Density Matrix ◽  
Lower Bounds ◽  
Multipartite Entanglement ◽  
Zero Temperature ◽  
Mixed States ◽  
X State ◽  
Computational Basis ◽  
Genuine Multipartite Entanglement

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.

scholarly journals COMPLEMENTARITY IN GENERIC OPEN QUANTUM SYSTEMS

2010 ◽  
Vol 24 (24) ◽  
pp. 2485-2509 ◽  
Author(s):  
SUBHASHISH BANERJEE ◽  
R. SRIKANTH
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Atomic Systems ◽  
Information Theoretic ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Difference ◽  
Positive Operator Valued Measure

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on entropy excess, X, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite-dimensional systems, a weighting of phase knowledge by a factor μ (> 1) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that μ tends to 1 as the system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for an oscillator as well as atomic systems.

scholarly journals Quantum Entanglement of Free Particles

2021 ◽  
Author(s):  
Roumen Tsekov
Keyword(s):  
Schrödinger Equation ◽  
Quantum Entanglement ◽  
Schrodinger Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Integral Of Motion ◽  
Friction Forces ◽  
Correlation Decay ◽  
Free Particles ◽  
Over Time

In this paper, the Schrödinger equation is solved for many free particles and their quantum entanglement is studied via correlation analysis. Converting the Schrödinger equation in the Madelung hydrodynamic-like form, the quantum mechanics is extended to open quantum systems by adding Ohmic friction forces. The dissipative evolution confirms the correlation decay over time, but a new integral of motion is discovered, being appropriate for storing everlasting quantum information.

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