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- (Color online) |A|2 is the probability of finding the spin system in the state |⇓↓〉. It
**oscillates**at the high**frequency**D (=2.88GHz). The**frequency**of the beats is χ/2 (=16.7MHz). The amplitude of**oscillations**is also modulated by an additional cosine wave signal of**frequency**χ (see text). |C|2 is the probability of finding the spin system in the state |0↓〉. It**oscillates**at the low**frequency**χ. It is almost zero in the time interval 90–100ns. The probability of finding spin system in the state |⇑↓〉, |B|2, has the same**oscillations**than |A|2 but it is anti-phase (see Fig. 3). ... Ideal truth table and schematic representation of a two-**qubit**CNOT gate irradiated by a sequence of two microwave π/2-pulses of equal width t and a variable waiting time between pulses τ. In the text, x and y are the states of two impurity spins of diamond, namely the spin-12 carried by the P1 center and the spin-1 carried by the NV−1 color center. The symbol ⊕ is the addition modulo 2, or equivalently the XOR operation. ... (Color online) NV−1 Rabi**oscillations**. Control**qubit**down: blue, red and green lines correspond, respectively, to the time evolution of |A|2, |B|2 and |C|2, i.e., the probabilities of finding the spin system in the state |⇓↓〉, |⇑↓〉 and |0↓〉. Control**qubit**up: red, blue and green lines represent, respectively, |A′|2, |B′|2 and |C′|2, i.e., the probabilities of finding the spin system in the state |⇓↑〉, |⇑↑〉 and |0↑〉, i.e., |A′|2=|B|2, |B′|2=|A|2 and |C′|2=|C|2 (see text). Fig. 4 gives details in the interval 60–120ns. They can also be revealed by a zoom in.Data Types:- Image
- Tabular Data

- Several quantum-mechanical correlations, notably, quantum entanglement, measurement-induced nonlocality and Bell nonlocality are studied for a two
**qubit**-system having no mutual interaction. Analytical expressions for the measures of these quantum-mechanical correlations of different bipartite partitions of the system are obtained, for initially two entangled**qubits**and the two photons are in their vacuum states. It is found that the**qubits**-fields interaction leads to the loss and gain of the initial quantum correlations. The lost initial quantum correlations transfer from the**qubits**to the cavity fields. It is found that the maximal violation of Bell’s inequality is occurring when the quantum correlations of both the logarithmic negativity and measurement-induced nonlocality reach particular values. The maximal violation of Bell’s inequality occurs only for certain bipartite partitions of the system. The**frequency**detuning leads to quick**oscillations**of the quantum correlations and inhibits their transfer from the**qubits**to the cavity modes. It is also found that the dynamical behavior of the quantum correlation clearly depends on the**qubit**distribution angle.Data Types:- Image

- (Color online.) Schematic diagram of the displaced
**oscillator**basis. The horizontal axis x′=x2mω0ℏ. All three wells maintain the same harmonic character, and usual eigenstates as well. The equilibrium position of the left (or the right) well is shifted by a specific constant. The shift direction is to the left (or right) when the**qubits**are in |+〉=|e1,e2〉 (or |−〉=|g1,g2〉). The middle potential well which is double degenerate corresponds to non-displaced case in which the states of the two**qubits**are opposite, i.e., |0〉 (|g1,e2〉 or |e1,g2〉), and the equilibrium position is higher than the others. The eigenstates which have the same value of n in the left well are degenerate with that in the right well. ... (Color online.) (a) Schematic diagram of the structure. The two light blue squares are improved three-junction flux**qubits**fabricated to the center conductor. (b) Schematic graph of the system. Two identical**qubits**(i.e. parameters Δ, ϵ, energy-level splitting Eq and coupling strength g for both**qubits**are of the same value) viewed as a two-level system with ground state |g〉 and excited state |e〉, are coupled to a harmonic**oscillator**whose characteristic**frequency**is ω0. ... (Color online.) Comparison between the displaced**oscillator**adiabatic approximation method and the numerical solution for the lowest two levels. ℏω0/Eq=10. The black solid lines stand for the lowest two energy levels calculated by adiabatic approximation. The green dashed line and the red dashed line correspond to the lowest two energy levels obtained by the numerical solution. (a) θ=0. (b) θ=π/6. (c) θ=π/4. (d) θ=π/3.Data Types:- Image

**Qubit**Data Types:- Image

- The sketch of the
**qubit**–detector systems considered in the paper. The**qubit**(two coupled quantum dots: x and y) is coupled electrostatically via U parameter with one of the detector QDs. Panels A, B and C correspond to the single-QD, double-QD and triple-QD detectors, respectively. ...**Qubit**QD occupations, nx(t), versus time for the DQD (TQD) detector – curves a–c (d, e) and for different initial conditions. Curves a and d:**qubit**is ‘frozen’ in the state nx=0,ny=1 until t=40 when the occupancies of all detector QDs achieve their steady state values. Curves b and e:**qubit**is ‘frozen’ in the state nx=0,ny=1 and also n2=n3=0 until t=40 when the occupancy of the first detector QD, n1, achieves its steady state value. Curve c: all couplings in the**qubit**–detector system are switched on at t=40 (i.e. nx=0,ny=1, n1=n2=0 for t<40). The other parameters: Vxy=4, U=4, Vij=0.5, Γ=1, εi=0 and μL=−μR=20. ... Charge**qubit**... The nearby**qubit**QD occupation, nx(t), as a function of time for the triple-QDs detector shown in Fig. 1C for different values of the**qubit**tunneling amplitude Vxy=1,2 and 4, respectively. The upper (bottom) panel corresponds to μL=−μR=1 (μL=−μR=10). The other parameters are εi=0, V12=V23=1, Vxy=4, U=4 and the initial conditions as in Fig. 2. ... Nearby**qubit**QD occupation, nx(t), as a function of time for the triple-QD detector (see Fig. 1C) for different values of U parameter: U=0,2,3,4 and 6, respectively. The bias voltage μL=−μR=10, other parameters and initial conditions as in Fig. 6. ... Nearby**qubit**QD occupation, nx(t), as a function of time for different forms of the detector depicted in Fig. 1. The upper (bottom) panel corresponds to the ΓL=ΓR=Γ=1 (Γ=0.2). The tunneling coupling between QDs is V=1 for the detector and Vxy=4 for the**qubit**, energy levels of all QDs are equal to εi=0, μL=−μR=10 and U=4. The**qubit**was ‘frozen’ in the configuration nx=0, ny=1 for t<15, i.e. until the detector QD occupancies and currents jL and j12 achieved their stationary values. The curves B and C are shifted down by 1 and 2 for clarity. ...**Qubit**dynamicsData Types:- Image

- Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉, the
**oscillator**initially in the number state |1〉 and qubit2 initially in a maximally mixed state, p=0.5 for a longer time-scale, with λ1=1.0 and λ2=0.1. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the**oscillator**initially in a binomial state with M=7 and q=0.85. In this case qubit2 is decoupled, λ2=0.0 and λ1=1.0. ... Plot of the linear entropy ζ (as a function of t) of a**qubit**initially in state |e〉 and the**oscillator**initially in the mixed state ρosc(0)=f|0〉〈0|+(1−f)|1〉〈1| with λ=1.0 and f=0.5. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the**oscillator**initially in a binomial state with M=11 and q=0.95. In this case qubit2 is coupled to the**oscillator**, with λ2=0.1, λ1=1.0, and p=0.5. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the**oscillator**initially in a binomial state with M=100 and q=0.1. In this case qubit2 is decoupled, λ2=0.0 and λ1=1.0.Data Types:- Image

- a) Ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron
**frequency**ωC for α = 7.0; F = 105.5; l0 = 0.45. ... (a) ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron**frequency**ωC for F = 105.0; l0 = 0.45; β = 0.8;. ... Transition**frequency**ω as a function of the cyclotron**frequency**ωc for (a) F = 105.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (b) α = 7.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (c) α = 7.0; F = 105.5; β = 0.8; ϑ = π/2; φ = 2π, (d) α = 7.0; F = 105.5; l0 = 0.45; ϑ = π/2; φ = 2π. ... a) ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron**frequency**ωC for α = 7.0; l0 = 0.45; β = 0.8. ... Period of**oscillation**τ as a function of the cyclotron**frequency**ωC for (a) F = 105.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (b) α = 7.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (c) α = 7.0; F = 105.5; β = 0.8; ϑ = π/2; φ = 2π, (d). α = 7.0; F = 105.5; l0 = 0.45; ϑ = π/2; φ = 2π.Data Types:- Image

- Schematic representation of the systems of a single
**qubit**and two**qubits**interacting with the single electron transistor. The wavy lines correspond to the Coulomb interaction of electrons localized on the nearest quantum dots. ... The asymptotic current JL(t=∞) tunneling between the left lead and the SET QD against the pulse duration τ which determines the coherent**qubit**evolution (for details, see the text). The curve A (B, C, D, E) corresponds to the system of one (two)**qubit**coupled with the SET. The curve B (C) describes the case when the electron tunneling amplitude V inside one (both)**qubit**has a shape of the rectangular pulse of duration τ. The curve D (E) corresponds to the case when the pulse durations in the first and second**qubits**are equal τ and 2τ, respectively. εi=0,i=1,2,3,4,5; U1=U2=2, V=1 and μL=-μR=5. ... The probability n4(t) of finding the electron in the nearby**qubit**QD against the time in the case of two**qubits**coupled with the SET. The thin, thick and broken curves correspond to the bias voltage Vb=0,2 and 4, respectively. μL=-μR, U1=0.5, U2=1 and the other parameters are as in Fig. 5. ... The probability n3(t) of finding the electron in the nearby**qubit**QD and the current tunneling between the left lead and the SET QD against the time, the upper and lower panels, respectively. The left (right) panels correspond to one**qubit**(two**qubits**) coupled with the SET. The thin solid line describes the**qubits**with the constant electron energy levels, ε2=-ε3=ε4=-ε5=-1, and the thick, solid and broken lines correspond to harmonically driven energy levels with the amplitude Δ=1 and 2, respectively. ε1=0, μL=2, μR=-2, U1=U2=5, n3(0)=n5(0)=1, n1(0)=n2(0)=n4(0)=0. ... The probabilities n3(t) and n5(t) (the upper panels) of finding electrons in the far-removed**qubit**QDs against the time for the case of two**qubits**coupled with the SET. In the lower panel the current JL(t) tunneling between the left lead and the SET QD against the time is displayed. ε1=2, ε2=ε3=ε4=ε5=0, V1=V2=1, U1=U2 and μL=-μR=0.5. ... Charge**qubit**Data Types:- Image

- Flux
**qubit**... Example of the dynamics for the symmetric case ε=0, where the**oscillator****frequency**is in resonance with the TSS**frequency**, i.e., Ω=Δ0. Parameters are: g=0.18Δ0, κ=0.014 (→α=0.004), kBT=0.1ℏΔ0. QUAPI parameters are M=12, K=1, Δt=0.06/Δ0. ... Sz(ω) for two values of the**oscillator****frequency**Ω. Parameters are: ε=0, g=0.07Δ0, κ=0.014, kBT=0.1ℏΔ0. ... Main: Dephasing rates corresponding to peak 1 and peak 2 in the Figs. 1 and 3 as a function of the HO**frequency**Ω. The parameters are: ε=0, g=0.07Δ0, κ=0.014, kBT=0.1ℏΔ0. Inset: Same for stronger damping κ=0.02 with α=0.01=const. (like in [15]). This implies that with varying Ω also g is changed.Data Types:- Image

**Qubit**... The relational curves of the**oscillation**period T of the**qubit**to the electron-LO-phonon coupling constant α and the polar angle θ. ... The**oscillation**period T changes with the confinement length l0 and the electron-LO-phonon coupling constant α. ... The relational curves of the**oscillation**period T to the confinement length l0 and the polar angle θ.Data Types:- Image

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