IN THE CONTEXT OF TIME-INDEPENDENT PARAMETERS IN TWO QUANTUM SYSTEMS: QUANTUM ENTANGLEMENT AND CORRELATIONS WITH NEGATIVITY MEASUREMENT

In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.

Anahtar Kelimeler:

reduced density matrix, Probability amplitudes

IN THE CONTEXT OF TIME-INDEPENDENT PARAMETERS IN TWO QUANTUM SYSTEMS: QUANTUM ENTANGLEMENT AND CORRELATIONS WITH NEGATIVITY MEASUREMENT

Keywords:

Interaction between ion and phonons, , Reduced density matrix, , Probability amplitudes , Entanglement,

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[1] Heisenberg W. The Physical Principles of the Quantum Theory. Dover Publications, New York, NY, USA, 1930.
[2] Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 1935; 47: 777-780.
[3] Bohr N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 1935; 48: 696-702.
[4] Schördinger E. Die gegenwrtige situation in der quantenmechanik. Naturwissenschaften. 1935; 23: 807-812.
[5] Hitoshi I. Quantum measurement cannot be a local physical process, journal of quantum ınformation science. 2019;9:171-178.
[6] Landsman KA, Wu Y, Leung PH, Zhu D, Linke NM, Brown KR, Duan LM, Monroe C. Two-qubit entangling gates within arbitrarily long chains of trapped ions. Phys. Rev. A. 2019; 100: 02:2332.
[7] Muhammed A. Qualitative aspects of the entanglement in the three-level model with photonic crystals. App. Phys. B. 2005; 81; 193-203.
[8] Wong-Campos JD, Moses SA, Johnson KG, Monroe C. Demonstration of two-atom entanglement with ultrafast optical pulses. Phys. Rev. Lett. 2017; 119: 23: 0501.
[9]Wootters WK. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev Lett. 1998; 80; 2245-2248.
[10] Guha MM. Quantum information processing using the exchange interaction. Journal of Quantum Information Science. 2018; 8; 139-160.
[11] Dermez R, Deveci B, Güney DO. Quantum dynamics of a three-level trapped ion under a time-dependent interaction with laser beams. Eur. Phys. J. D. 2013; 67: 120.
[12] James DFV. Quantum computation and quantum information theory. Appl. Phys. B. 1998; 66: 181-190.
[13] Monreo C, Meekhof DM, King BE, Wineland DJ. A Schrödinger cat superposition state of an atom science. 1996; 272: 5265: 1131-1136.
[14] Dermez R, Özen S. Higher dimensional entangled qudits in a trapped three-level ion. Eur. Phys. J. D. 2010;57: 431-437.
[15] Yu GY, Du S, Li X, Wu S. Entangled bases with fixed Schmidt number. Journal of Physics A: Mathematical and Theoretical. 2015; 48: 24: 245301.
[16] Dermez R, Müstecaplıoğlu ÖE. Long-lived entangled qudits in a trapped three-level ion beyond the Lamb–Dicke limit. Phys. Scr. 2009; 71: 015304.
[17] Nieuwenburg E, Zilberberg O. Entanglement spectrum of mixed states. Phy. Rev. A. 2018; 98: 012327.
[18] Neumann J. Mathematical Foundations of Quantum Mechanics. Princeton Uni. Press, NJ, USA: 1995.
[19] Dermez R. Concurrence and negativity as a family of two measures elaborated for pure qudit states. Journal of Russian Laser Research. 2017; 38: 408-415.
[20] Zheng SB, Kuang LM,Gao KL. Two-mode squeezed states and their superposition in the motion of two trapped ions. Phys. Lett. A. 2002; 300, 427-431.
[21] Zheng S.B. Preparation of motional macroscopic quantum-interference states of a trapped ion. Phys. Rev. A. 1998; 58: 761.
[22] Zheng S.B. Control of motional states of a trapped ion. Phys. Lett. A 1998; 248, 25-28.
[23] Müstecaplıoğlu ÖE. Motional macroscopic quantum superposition states of a trapped three-level ion. Phys. Rev. A. 2003;68: 023811.
[24] Sakurai JJ. Modern Quantum Mechanics. Addison-Wesley Publishing Company, USA: 1994.
[25] Vidal G, Werner RF. Computable measure of entanglement. Phys. Rev. A. 2003; 65: 032314.
[26] Lee S, Chi DP, Oh SD, Kim J. Convex-roof extended negativity as an entanglement measure for bipartite quantum systems. Phys. Rev. A. 2003; 68: 062304.
[27] Dermez R. Generalized concurrence and negativity in time-dependent C3⊗C5= C15 dimensional ionic–phononic systems. Journal of Russian Laser Research. 2016;37: 572-580.
[28] Dermez R. Comparing concurrence and negativity in time-dependent ionic-phononic system with fifteen dimensional density matrix. IOP Publishing Journal of Physics: Conference Series 766, 2016: 012012.
[29] Anvar SJ, Ramzan M, Khan MK. Dynamics of entanglement and quantum Fisher information for N-level atomic system under intrinsic decoherence. Quantum Information Process. 2017;16:142.
[30] Liao QH, Wu JF, Wang P. Properties of entanglement between the two trapped ions. Indian J. Phys. 2017; 91: 12: 1615-1624.