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By investigating the coherence of up to 8 ions over time, we observe a.Journal Article: 14-Qubit Entanglement: Creation and Coherence Citation Details In-Document Search 14-Qubit Entanglement. DECAY; NOISE; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUBITS COMPUTERS; INFORMATION; Word Cloud. Our results demonstrate that the two-qubit entanglement generally decreases as increases. We show analytically that, in the limit, no entanglement can be created. This indicates that collective thermal environments cannot create two-qubit entanglement when. Direct measurement of the entanglement of two superconducting qubits via state tomography. S /h in the spectroscopy of the individual qubits14. The performance of each qubit can be determined separately by strongly detuning the two qubits relative toS /h. Creation of Two- Particle Entanglement in Open Macroscopic Quantum Systems. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider an open quantum system of not directly interacting spins (qubits) in contact with both local and collective thermal environments. The. qubit- environment interactions are energy conserving. We trace out the variables. We numerically simulate the reduced. Our results demonstrate that the two- qubit entanglement generally decreases as increases. This indicates that collective thermal environments cannot create two- qubit. We discuss possible relevance of our consideration. Introduction. In open many- body systems, such as solid- state and biological ones, quantum behavior reveals itself in many ways. Often the quantitative parameter used to measure . The presence of entanglement implies that the wave function (or the reduced density matrix) cannot be represented as a product of the corresponding objects for the individual qubits. It is important to note that to produce and to measure entanglement in such systems, one does not necessarily need to know much detail about the system, possibly not even its Hamiltonian . The questions then are how useful is entanglement as a measure of quatumness, what can it add to our knowledge of system properties and behavior, and how can it be utilized? Indeed, just knowing that the system is entangled (knowledge of complicated quantum behavior) is not sufficient to imply that its quantum properties are useful for specific applications. Fortunately, however, in some situations entanglement provides very useful properties, including additional exponential resources for quantum computation . This interaction should be of a . Many aspects of entanglement creation are widely discussed in the literature (See, e. Entanglement can then still be created merely by the indirect interaction of noninteracting qubits through a collective thermal bath. It was demonstrated numerically in . The conditions for entanglement creation were discussed and analyzed numerically in . It was concluded that, in spite of the competition between the local thermal environments (which destroy entanglement) and the collective thermal environment (tending to create entanglement), the creation of measurable entanglement can be realized for some finite times. As was recently shown in . 14 qubit register D-Wave claims to have developed quantum annealing and introduces their product called D-Wave One. The company claims this is the first commercially available quantum computer. 14-qubit entanglement: Creation and coherence. CAS ADS PubMed Article Aoki, T. PDF files Supplementary Information (850kb) Supplementary Information Additional data Science jobs NatureJobs.com. The qubits interact with both local and collective thermal environments (all at the same temperature). The collective interaction introduces an indirect qubit interaction. In the total density matrix of all qubits and environments, we trace over the variables of the environments and qubits. This gives us the time- dependent reduced density matrix for two arbitrary qubits. In the - representation it is represented by a time- dependent matrix. It is important to notice that the matrix elements, , , depend not only on the parameters of the thermal environments but also on the total number of qubits, . We study numerically the concurrence of the reduced two qubit density matrix and its dependence on the parameters of the system and on . To realize and study this situation in an experiment, one must have access to the two selected qubits (such as their particular frequencies), in order to manipulate them and prepare the initial state. Our main result is that the amplitude of concurrence, , generally decreases as increases. This means that one should not expect that the collective thermal environment can create by itself measurable entanglement even of two qubits, in the presence of many other qubits within the range of the collective environment coherence length. Outline of Main Results. The initial state of the entire system is disentangled, a product state in which each of the spins is in a state , ; all local reservoir states are thermal and so is that of the collective reservoir, at a fixed common temperature (A generalization to a nonequilibrium situation where each local and the collective reservoir have different individual temperatures is immediate.). Analytic Results (i) Explicit Dynamics. As the spins interact with the reservoirs via energy- conserving couplings only, the reduced two- spin dynamics can be calculated explicitly; see Proposition 2. Consequences of the energy conservation are that populations, that is, the diagonal density matrix elements, are time independent and that the off- diagonal elements evolve independently. As an example, we discuss here the dynamics of the (1, 2) matrix element. The other matrix elements have similar behavior. Each factor on the r. None of the other initial matrix elements are involved (energy- conserving coupling).(ii) is the uncoupled dynamics (no interaction with environments); (iii) is a dephasing factor with a time- dependent phase becoming linear for large (for the considered infrared behavior of the coupling constants in three dimensions, see (2. Both the local and collective reservoirs contribute; however, the term is independent of the traced- out spins (again, it would be the same if only two spins were coupled to the reservoirs); (v) is a product of oscillating terms encoding the effect of all the traced- out spins (see (2. It is important to notice that . Consequently, the two- qubit state does not depend on the initial off- diagonal density matrix elements of the traced- out . Typically, we expect those spins to be initially in (close to) equilibrium, corresponding to vanishing off- diagonals. Some general properties of can be explained easily for the case in which all spins are initially in the high- temperature equilibrium state . Then and its magnitude oscillate between zero and one. Due to the large power , the peaks of the function , centered at the discrete times satisfying , are of very narrow width for large . Consequently, in the limit , with held fixed, is zero for all except for , where . But the density matrix becomes very simple if , because many entries vanish (c. Proposition 2. 1) and the corresponding concurrence is zero. It follows that, in the large limit, concurrence is zero for all times (except possibly for some isolated instances, ).(ii) - Dependent Scaling of the Interaction The above analysis suggests that one cannot generate two- spin entanglement for large at fixed interaction strength . However, the width of the peaked function which is of order becomes appreciable if . Hence we consider an - dependent scaling of the coupling, replacing by , for some . According to the above discussion, the borderline case is . Starting from the explicit expressions (Proposition 2. The analytic expressions we obtain for and show that the limiting dynamics does not create entanglement, for any time . While we are able to obtain explicit expressions for concurrence in the regime of , we are not so for finite. We study this decay numerically. In the simulations, we take of the order of the thermal frequency . In the infra- red regime, our coupling is proportional to (see after (2. For , concurrence creation is maximal if both spins start out in their high- temperature state ; see Figure 1. Consequently, in the subsequent simulations, we take initial states of the two not traced- out qubits very close to this state, and we take the diagonals of the initial states of the traced- out quibts to be constant (remember that the off- diagonals of these qubits do not influence the dynamics at all). In Figure 4 we modify the initial state of the two not traced- out qubits and check that maximal concurrence is indeed obtained when both qubits are in the above state, even for large . Figure 1: Maximal concurrence as a function of and , for fixed ans . Here, spins is considered. For general , entanglement evolves according to a rescaled time , see Figure 2. This figure shows that a reduction of diminishes the created concurrence in a moderate way. For instance, decreasing by a factor only decreases concurrence by less than . Figure 2: (a) Concurrence as a function of the rescaled time, for different and fixed , being respectively the cut- off and thermal frequency ( with ) and the form factor . Other values are the same as in (a). In Figure 3 we show that the maximum of created concurrence decays with increasing . For intermediate values of (with the current parameters N~1. The dashed line is the best fit with . Figure 4: Maximal concurrence as a function of the independent parameters, and . As one can see the maximal concurrence is realized at the external corner, that is . Here is , and for all other spins. We have found that this time decays exponentially in the number of spins, , for sufficiently large . Results on the rescaled model are shown in Figure 5. We find a decrease of maximal concurrence with increasing for all . The critical value, (see analytic results above), divides the concurrence decay into two regimes. In the range, , the maximal concurrence decreases exponentially in , for intermediate values of (between 1. For the decay is superexponential and varies with . We conclude that no scaling can compensate the decay of created concurrence for large . Figure 5: Maximal concurrence as a function of the number of spins, for different power law scaling, as indicated in the legend. The dashed line indicates a fitting exponential for the cases . The solid curve indicates the case, . Model and Reduced Density Matrix. The full Hamiltonian of the noninteracting spins coupled by energy conserving interactions to local and collective bosonic heat reservoirs is given by. Below we use dimensionless variables and parameters. To do so, we introduce a characteristic frequency, , typically of the order of spin transition frequency. The total Hamiltonian, energies of spin states, and temperature are measured in units . |
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December 2016
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