Sensitivity of entanglement decay of quantum-dot spin qubits to the external magnetic field

Abstract

We study the decay of entanglement of quantum dot electron-spin qubits under hyperfine interaction mediated decoherence. We show that two qubit entanglement of a single entangled initial state may exhibit decay characteristic of the two disentanglement regimes in a single sample, when the external magnetic field is changed. The transition is manifested by the supression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence (which result in oscillatory behaviour of entanglement sudden death time as a function of the magnetic field). This unique behaviour allows us to propose the double quantum dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic field.Systems of electron spins confined in quantum dots (QDs) have received much theoretical (see for review) and experimental (see for review) interest since the initial proposal for spin-based quantum computing [7]. This resulted in the development of a range of effective techniques for the initialization, manipulation, and readout of the spin state in two main trends. One, involving electrical (or magnetic) manipulation of lateral QDs [8][9][10], and the other, involving optical manipulation of self-assembled QDs [11][12][13]. Both prove sucessful in the generation of high fidelity initial states, also entangled, but the coherent evolution of spin states and manipulation thereof suffer from the destructive effects of the hyperfine interaction between the electron spin and the spins of the nuclei of the QD atoms. Hence, the current experiments focus mostly on few-spin qubits [14,15] which are more robust against decoherence, or on involved schemes for the minimization of decoherence effects [16][17][18]. The proficiency attained in the experiments has been very recently demonstrated in Ref. [19], where quantum state tomography of two initially entangled singlet-triplet qubits has been performed.The central idea of this paper is to propose, based on the high level of the experimental techniques used to study electron spin states in QDs, a scheme for sensing an external parameter (the magnetic field) by harnessing the entanglement present in a two-qubit system and the inbuilt decoherence processes. The idea is outside of traditional methods in quantum metrology, since it relies on decoherence, while metrology requires a high degree of quantum coherence. It is vital that the qubits be electron spins confined in QDs with a non-zero nuclear spin of the environment, because this leads to the specific system-environment interaction and results in a characteristic disentanglement process, which, as we have found, strongly and counter-intuitively depends on the magnetic field.The study of spin entanglement [20] decay in a twoelectron-two-QD system, has up-to-date been limited to a number of complex, yet solvable scenarios [21][22][23]. The complexity accounts for the nontrivial behavior of the reported evolution of entanglement. Hence, in Refs [21] ...

Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots

“…The results for C(t) and t D (Ω) in the thermal bath case were previously obtained in Ref. 80, where it was suggested that a measurement of t D can be used for sensing of small magnetic fields, while in Refs. 115 and 116 the possible significance of entanglement dynamics for the operation of chemical magnetometers was discussed.…”

“…where K Q σξ,ξ ′ σ ′ (t) encapsulates the influence of the environment on the evolution of the reduced density matrix of qubit Q. The above representation 80,105,106 is of course closely related to the operator-sum (Kraus) representation of evolution ofρ Q , but it is much more convenient to use when the number of relevant Kraus operators is large (as it is the case here). The K functions have the following structure:…”

“…Here we consider uncoupled spins (∆ ST = 0) and focus on B = 0 (with most attention devoted to regime of fields larger than the typical Overhauser field generated by the coupling to the nuclei). In two recent works 80,81 both entanglement and more general quantum correlations were considered for two uncoupled spin qubits freely evolving at rather smalls B fields (including B = 0), and interacting with thermal nuclear baths. Here we consider other bath states (narrowed, correlated), and we also calculate the entanglement dynamics under application of the spin echo protocol.…”

Decoherence-enhanced quantum measurement of a quantum-dot spin qubit

“…This is especially im portant in the m easurem ent o f nanostructures em bedded in the solid state, w here decoherence resulting from the interaction with the environm ent is unavoidable. A lthough decoherence typically leads to the destruction o f quantum effects, there are som e situations when decoherence can be helpful (e.g., to facilitate electron transport in quantum -dot (QD) chains [3,4]) and may even be utilized for m easurem ent purposes [5,6].…”

How to detect qubit environment entanglement in pure dephasing evolutions

“…as a measure of entanglement for the class of systems described previously, or, more generally, for any state that can be written in the form (3), as such states can be sometimes obtained for different classes of Hamiltonians under specific conditions for the initial state [35]. Here a and b are the coefficients of the initial qubit superposition, while the function…”