Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond

Nandi, Sumit; Datta, Chandan; Das, Arpan; Agrawal, Pankaj

doi:10.1140/epjd/e2018-90252-2

Cited by 6 publications

(3 citation statements)

References 19 publications

(35 reference statements)

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“…Thus, the analysis on this four-level system is very similar to that already performed in the previous example: the basic difference is the presence of contributions related to the states |0 and |3 with equal weights. Figure 3 The solution established for the visualization difficulty related to the discrete SU(2)⊗SU(2) Wigner functions has, in the correspondence with four-level systems, an effective mathematical tool in the study of maximally entangled mixed states [56][57][58][59] where, in particular, the two-qubit X-states take a special place [24,[62][63][64][65][66][67]. Next, we will explore this fact to characterize the maximally entangled mixed two-qubit X-states through the discrete SU(4) Wigner functions.…”

Section: Revisiting Two-qubit Bell and Werner Statesmentioning

confidence: 99%

Representations of two-qubit and ququart states via discrete Wigner functions

Marchiolli,

Galetti

2019

Preprint

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By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group SU(N), it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete phase spaces which has the discrete SU(N) Wigner function as a legitimate by-product. In this paper, we apply these results with the aim of putting forth a detailed study on the discrete SU(2) ⊗ SU(2) and SU(4) Wigner functions, in straight connection with experiments involving, among other things, the tomographic reconstruction of density matrices related to the two-qubit and ququart states. Next, we establish a formal correspondence between both the descriptions that allows us to visualize the quantum correlation effects of these states in finite-dimensional discrete phase spaces. Moreover, we perform a theoretical investigation on the twoqubit X-states, which combines discrete Wigner functions and their respective marginal distributions in order to obtain a new function responsible for describing qualitatively the quantum correlation effects. To conclude, we also discuss possible extensions to the discrete Husimi and Glauber-Sudarshan distribution functions, as well as future applications on spin chains.

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Section: Revisiting Two-qubit Bell and Werner Statesmentioning

confidence: 99%

Representations of two-qubit and ququart states via discrete Wigner functions

Marchiolli,

Galetti

2019

Preprint

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“…Uhlmann and Jozsa's papers are considered classic fidelity studies [12][13][14]. Fidelity, negativity, purity, and concurrence are popular methods for quantum entanglement [15][16][17]. A structure worthy of study is presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Two measures elaborated for entangled states: Quantum entropy and fidelity using Schmidt coefficients of the reduced density matrix of full TRI

Dermez

Tunçer

2022

Rev. Mex. Fís.

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In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two critical measures. The findings obtained in this study showed that the maximum value of fidelity for entangled states is quantified approximately to be 0.35, and the long lifetime is also observed with entropy measurement. The findings suggest that three coupling parameters play a significant role in developing quantum entanglement.

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“…The latest studies on the linear dimer system study both its spectroscopy [2] and stabilization by complexation with a Lewis acid. [3] The monomer has also been of great interest to those studying pre-biotic chemistry [4][5][6][7][8] due to the fact that its reactive polymerization can lead to the formation of simple amino acids via diaminomaleonitrile, [7] a tetramer of HCN.…”

Section: Introductionmentioning

confidence: 99%

Fundamental Vibrational Analyses of the HCN Monomer, Dimer and Associated Isotopologues

et al. 2018

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In this work we provide high level ab initio treatments of the structures, vibrational frequencies, and electronic energies of the HCN monomer and dimer systems along with several isotopologues. The plethora of information related to this system within the literature is summarized and serves as a basis for comparison with the results of this paper. The geometry of the dimer and monomer are reported at the all electroncoupled-cluster singles, doubles, and perturbative triples level of theory [AE-CCSD(T)] with the correlation consistent quadruple-zeta quality basis sets with extra core functions (cc-pCVQZ) from Dunning. The theoretical geometries and electronic structures are further analyzed through the use of the Natural Bond Orbital (NBO) method and Natural Resonance Theory (NRT). At the AE-CCSD(T)/cc-pCVQZ level of theory, the full cubic with semi-diagonal quartic force field for nine dimer and four monomer isotopologues (the parent isotopologue along with 15 N, 13 C, and D derivatives) were obtained to treat the anharmonicity of the vibrations via second order vibrational perturbation theory (VPT2). Lastly, the enthalpy change associated with the formation of the dimer from two monomer units was determined using the focal point analysis. Computations including coupled-cluster through perturbative quadruples as well as basis sets up to six-zeta quality, including core functions (cc-pCVXZ, X=D,T,Q,5,6) were used to extrapolate to the AE-CCSDT(Q)/CBS energy associated with this hydrogen-bond forming process. After appending anharmonic zero-point vibrational, relativistic, and diagonal Born-Oppenheimer corrections, we report a value of À3.93 kcal mol À1 for the enthalpy of formation. To our knowledge, each set of results (geometries, vibrational frequencies, and energetics) reported in this study represents the highest-level and most reliable theoretical predictions reported for this system.

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Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond

Cited by 6 publications

References 19 publications

Representations of two-qubit and ququart states via discrete Wigner functions

Representations of two-qubit and ququart states via discrete Wigner functions

Two measures elaborated for entangled states: Quantum entropy and fidelity using Schmidt coefficients of the reduced density matrix of full TRI

Fundamental Vibrational Analyses of the HCN Monomer, Dimer and Associated Isotopologues

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