Reply to “Comment on ‘Separability of completely symmetric states in a multipartite system’ ”

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Yi Shen ◽  
Lin Chen ◽  
Lilong Qian ◽  
Delin Chu
Keyword(s):  
Multipartite System ◽  
Symmetric States

scholarly journals Separability of completely symmetric states in a multipartite system

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
Lin Chen ◽  
Delin Chu ◽  
Lilong Qian ◽  
Yi Shen
Keyword(s):  
Multipartite System ◽  
Symmetric States

SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 415-422
Author(s):  
D. SALGADO ◽  
J. L. SÁNCHEZ-GÓMEZ ◽  
M. FERRERO
Keyword(s):  
Pure State ◽  
Convex Combination ◽  
Quantum States ◽  
Necessary Condition ◽  
New Approach ◽  
Product Matrix ◽  
Separability Problem ◽  
Multipartite System ◽  
Arbitrary Dimensions ◽  
Bipartite Case

We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state ρ in terms of a state Cρ with the same rank and another one Eρ with lower rank is perfomed, with weights 1 − λρ and λρ, respectively. Secondly a scalar [Formula: see text] is computed. Then ρ is separable if, and only if, [Formula: see text]. The computation of [Formula: see text] has been undergone under the simplest choice for Cρ as a product matrix and Eρ being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when Eρ is not pure in the bipartite case.

Quantum cloning of identical mixed qubits

2007 ◽  
Vol 7 (5&6) ◽  
pp. 551-558
Author(s):  
H. Fan ◽  
B.-Y. Liu ◽  
K.-J. Shi
Keyword(s):  
Upper Bound ◽  
Quantum Cloning ◽  
Single Qubit ◽  
Antisymmetric State ◽  
Pure States ◽  
Symmetric States

Quantum cloning of two identical mixed qubits $\rho \otimes \rho$ is studied. We propose the quantum cloning transformations not only for the triplet (symmetric) states but also for the singlet (antisymmetric) state. We can copy these two identical mixed qubits to $M$ ($M\ge 2$) copies. This quantum cloning machine is optimal in the sense that the shrinking factor between the input and the output single qubit achieves the upper bound. The result shows that we can copy two identical mixed qubits with the same quality as that of two identical pure states.

Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states

2014 ◽  
Vol 14 (11&12) ◽  
pp. 937-948
Author(s):  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Separable States ◽  
Qubit System ◽  
Symmetric States

In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

WEAKLY INTERACTING SYMMETRIC AND ANTI-SYMMETRIC STATES IN THE BILAYER SYSTEMS

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1511-1518 ◽  
Author(s):  
M. MARCHEWKA ◽  
E. M. SHEREGII ◽  
I. TRALLE ◽  
G. TOMAKA ◽  
D. PLOCH
Keyword(s):  
Experimental Data ◽  
Wave Functions ◽  
Charge Carriers ◽  
Landau Levels ◽  
Quantum Beats ◽  
Weakly Interacting ◽  
Symmetric Wave ◽  
Sdh Oscillations ◽  
Magnetic Filed ◽  
Symmetric States

We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

Chiralvs. symmetric states in optical isomers

1993 ◽  
Vol 15 (4) ◽  
pp. 621-629
Author(s):  
V. M. Pérez-García ◽  
I. Gonzalo ◽  
J. L. Pérez-Díaz
Keyword(s):  
Optical Isomers ◽  
Symmetric States
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