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1.
We discuss the entanglement properties of symmetric states of n qubits. The Majorana representation maps a generic such state into a system of n points on a sphere. Entanglement invariants, either under local unitaries (LU) or stochastic local operations and classical communication (SLOCC), can then be addressed in terms of the relative positions of the Majorana points. In the LU case, an overcomplete set of invariants can be built from the inner product of the radial vectors pointing to these points; this is detailed for the well-documented three-qubits case. In the SLOCC case, a cross ratio of related M?bius transformations are shown to play a central role, exemplified here for four qubits. Finally, as a side result, we also analyze the manifold of maximally entangled 3 qubit state, both in the symmetric and generic case. 相似文献
2.
We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |?,n> with ?=1,…,[n/2] are inequivalent under SLOCC. 相似文献
3.
Ishizaka S 《Physical review letters》2004,93(19):190501
I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose. 相似文献
4.
5.
Y. Cao A. M. Wang 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,44(1):159-166
We classify 4-qubit pure states under the stochastic
local operation and classical communication (SLOCC). There exist
twenty three essentially different classes of states, giving rise to
a four-graded partially ordered structure. We also give the
criterion to judge which class an arbitrary 4-qubit state belongs
to. We re-classify the 4-qubit pure state into 2×2×4,
4×4 aspects. Finally, we give our analysis of the
classification difference of methods for the 3-qubit pure state. 相似文献
6.
Sayatnova Tamaryan 《Physics letters. A》2011,375(23):2224-2229
Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement. 相似文献
7.
Daniel Armand-Ugon Rodolfo Gambini Octavio Obregón Jorge Pullin 《Nuclear Physics B》1996,460(3):615-631
We study several aspects of the canonical quantization of supergravity in terms of the Ashtekar variables. We cast the theory in terms of a GSU(2) connection and we introduce a loop representation. The solution space is similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the GSU(2) Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which coincides exactly with the Dubrovnik version of the Kauffman polynomial. This provides for the first time the possibility of finding explicit analytic expressions for the coefficients of that knot polynomial. 相似文献
8.
《中国物理 B》2019,(10)
We investigate the robustness of entanglement for a multiqubit system under dephasing and bit flip channels. We exhibit the difference between the entanglement evolution of the two forms of special states, which are locally unitarily equivalent to each other and therefore possess precisely the same entanglement properties, and demonstrate that the difference increases with the number of qubits n. Moreover, those two forms of states are either the most robust genuine entangled states or the most fragile ones, which confirm that local unitary(LU) operations can greatly enhance the entanglement robustness of n-qubit states. 相似文献
9.
《Physics letters. A》2006,359(5):428-437
We put forward an alternative approach to the SLOCC classification of three-qubit and four-qubit systems. By directly solving matrix equations, we obtain the relations satisfied by the amplitudes of states. The relations are readily tested since in them only addition, subtraction and multiplication occur. 相似文献
10.
A. V. Kats 《JETP Letters》2003,77(12):657-661
The intriguing problem of the “missing” MHD integrals of motion is solved in this paper; i.e., analogues of the Ertel, helicity, and vorticity invariants are obtained. The two latter have been discussed earlier in the literature only for specific cases, and the Ertel invariant is presented for the first time. The set of ideal MHD invariants obtained appears to be complete: to each hydrodynamic invariant corresponds its MHD generalization. These additional invariants are found by means of the fluid velocity decomposition based on its representation in terms of generalized potentials. This representation follows from the discussed variational principle in Hamiltonian (canonical) variables, and it naturally decomposes the velocity field into the sum of “hydrodynamic” and “ magnetic” parts. The “missing” local invariants are expressed in terms of the “ hydrodynamic” part of the velocity and therefore depend on the (nonunique) velocity decomposition; i.e., they are gauge-dependent. Nevertheless, the corresponding conserved integral quantities can be made decomposition-independent by the appropriate choice of the initial conditions for the generalized potentials. It is also shown that the Weber transformation of MHD equations (partial integration of the MHD equations) leads to the velocity representation coinciding with that following from the variational principle with constraints. The necessity of exploiting the complete form of the velocity representation in order to deal with general-type MHD flows (nonbarotropic, rotational, and with all possible types of breaks as well) in terms of single-valued potentials is also under discussion. The new basic invariants found allow one to widen the set of the local invariants on the basis of the well-known recursion procedure. 相似文献
11.
The full set of gauge-invariants is found for various gauge-fields interacting with matter fields (Higgs-fields). Both the dynamics and the canonical structure of the field are expressed in terms of invariants. Discrete invariants (like vortexes and monopoles) are discussed. 相似文献
12.
N. S. Baaklini 《Letters in Mathematical Physics》1977,2(1):43-47
The coupled spin-2-spin-3/2 system (supergravity) is obtained in Cartan's geometrical language of differential forms. The spin-3/2 field is introduced through a canonical spinor differential one-form. Two points are discussed: the introduction of higher spin fields and the origin of local supersymmetry. 相似文献
13.
Exact invariants and adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system 总被引:1,自引:0,他引:1
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The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results. 相似文献
14.
Letter: Active Gravitational Mass and the Invariant Characterization of Reissner–Nordström Spacetime
We analyse the concept of active gravitational mass for Reissner-Nordström spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do. 相似文献
15.
Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle. 相似文献
16.
研究了频率随时间变化的受迫谐振子系统的不变量和不变量的一般形式,并利用基本不变量构造了此含时系统的压缩态和压缩数态. 相似文献
17.
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states. 相似文献
18.
We investigate the equivalence of quantum states under local
unitary transformations. A complete set of invariants under local
unitary transformations are presented for a class of non-generic
three-qubit mixed states. It is shown that two such states in this
class are locally equivalent if and only if all these invariants
have equal values for them. 相似文献
19.
We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states. 相似文献
20.
Ting-Gui Zhang Ming-Jing Zhao Xianqing Li-Jost Shao-Ming Fei 《International Journal of Theoretical Physics》2013,52(9):3020-3025
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full rank mixed states with non-degenerate eigenvalues, this set of invariants is also the set of the necessary and sufficient conditions for the local unitary equivalence of such two states. 相似文献