Preparation of an arbitrary two-qubit quantum gate on two spins with an anisotropic Heisenberg interaction

Kuzmak, A. R.

doi:10.1142/s0219749918500442

Cited by 3 publications

(5 citation statements)

References 61 publications

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“…Using equations ( 69), ( 71) and ( 50), we can show that all terms containing Ĉ will vanish following exactly the same argument in equations ( 52) and ( 53) for the case of the system A; B, since Fp,q B shares exactly the same expression in both equations ( 46) and ( 69). Next we consider the free Hamiltonian for B where Ĥtot is expressed in the form of equation (54). We can express FÃ ;B in equation (69) as:…”

Section: Negativity Of System ã; Bmentioning

confidence: 99%

“…Next we consider the impact of the free Hamiltonian D for B where Ĥtot is given in equation (54). All terms in equation (77) containing the free Hamiltonian I A ⊗ D will also vanish, since when Âq = I A , the second part of equation (77) will become…”

Section: Free Hamiltonians Do Not Contribute To the Negativity Vulner...mentioning

confidence: 99%

“…We plot both the numerical calculations and the perturbative results to the second-order using equation (77). The red and blue (first two) curves mostly overlap, which suggests free Hamiltonians Ĉ and D do no contribute to the negativity vulnerability N 249) is the Heisenberg Hamiltonian that can generate the SWAP gate and interchange the states of two qubits at t = π 4 [54].…”

Section: C3 Negativity For ã; Amentioning

confidence: 99%

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The transfer of entanglement negativity at the onset of interactions

Yunfei

Kempf

2022

J. Phys. A: Math. Theor.

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Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement monotone negativity, we determine how the proclivity of an interaction to either generate, transfer or lose entanglement depends on the choice of Hamiltonians and initial states. These three proclivities are captured by Hamiltonian- and state-dependent quantities that we call negativity susceptibility, negativity transmissibility and negativity vulnerability respectively. These notions could serve, for example, as cost functions in quantum technologies such as machine-learned quantum error correction.

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Section: Negativity Of System ã; Bmentioning

confidence: 99%

Section: Free Hamiltonians Do Not Contribute To the Negativity Vulner...mentioning

confidence: 99%

Section: C3 Negativity For ã; Amentioning

confidence: 99%

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The transfer of entanglement negativity at the onset of interactions

Yunfei

Kempf

2022

J. Phys. A: Math. Theor.

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“…The technique which allows one to control and measure such systems is called the spin resonance technique [58,59]. Implementation of quantum states on different spin systems was widely studied in papers [60,61,62,63,64,65,66,67,68,69,70,71,19].…”

Section: Introductionmentioning

confidence: 99%

Entanglement of the Ising–Heisenberg diamond spin- 1/2 cluster in evolution

Kuzmak

2023

J. Phys. A: Math. Theor.

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In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chainshave been studied. Such spin structures are presented in various compounds. The ions of $Cu^{2+}$ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spins via Ising interaction. The influence of the interaction coupling with side spins on the entanglement of central spins is investigated. It is shown that choosing the value of this coupling allows us to control the behaviour of entanglement between central spins. As a result, we find conditions for achieving the maximal values of entanglement. In addition, the entanglement behaviour between the side spins, central and side spins, and between a certain spin and the rest of the system is studied. In these cases, the conditions for achieving maximal entanglement are also obtained.

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“…Therefore, a simplified version of this method was considered on the physical system of an atom having with a nuclear spin 1/2 and one valence electron. Using this method, the conditions for implementation of different quantum gates on the physical system of ultracold atoms in optical lattice was obtained in paper [52]. Experimental realization of a longdistance entangled state between spins in antiferromagnetic quantum spin chains was described in paper [53].…”

Section: Introductionmentioning

confidence: 99%

Implementation of a two-qubit state by an auxiliary qubit on the three-spin system

Kuzmak¹

2020

Phys. Scr.

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The method for preparation of a two-qubit state on two spins-1/2 that mutually interact through an auxiliary spin is proposed. The essence of the method is that, initially, the three spins evolve under the action of an external magnetic field during a predefined period of time. Then, the auxiliary spin is measured by a monochromatic electromagnetic radiation that allows obtaining a certain state of the remaining spins. We study the entanglement of this state and obtain the condition for achieving the maximally entangled state. The implementation of the method on the physical system of nuclear spins of xenon difluoride is described. As a results, the conditions which allow preparing the maximally entangled state on this system are obtained. S1S2 SC J J

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Preparation of an arbitrary two-qubit quantum gate on two spins with an anisotropic Heisenberg interaction

Cited by 3 publications

References 61 publications

The transfer of entanglement negativity at the onset of interactions

The transfer of entanglement negativity at the onset of interactions

Entanglement of the Ising–Heisenberg diamond spin- 1/2 cluster in evolution

Implementation of a two-qubit state by an auxiliary qubit on the three-spin system

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