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

Abstract

We study the dynamics of entanglement of two electron spins in two quantum dots, in which each electron is interacting with its nuclear spin environment. Focusing on the case of uncoupled dots, and starting from either Bell or Werner states of two qubits, we calculate the decay of entanglement due to the hyperfine interaction with the nuclei. We mostly focus on the regime of magnetic fields in which the bath-induced electron spin flips play a role, for example their presence leads to the appearance of entanglement sudden death at finite time for two qubits initialized in a Bell state. For these fields the intrabath dipolar interactions and spatial inhomogeneity of hyperfine couplings are irrelevant on the time scale of coherence (and entanglement) decay, and most of the presented calculations are performed using the uniform-coupling approximation to the exact hyperfine Hamiltonian. We provide a comprehensive overview of entanglement decay in this regime, considering both free evolution of the qubits, and an echo protocol with simultaneous application of $\pi$ pulses to the two spins. All the currently relevant for experiments bath states are considered: the thermal state, narrowed states (characterized by diminished uncertainty of one of the components of the Overhauser field) of two uncorrelated baths, and a correlated narrowed state with a well-defined value of the $z$ component of the Overhauser field interdot gradient. While we mostly use concurrence to quantify the amount of entanglement in a mixed state of the two electron spins, we also show that their entanglement dynamics can be reconstructed from measurements of the currently relevant for experiments entanglement witnesses, and the fidelity of quantum teleportation performed using a partially disentangled state as a resource.

23 pages, 13 figures, published version

References in corpus (42)

• Entanglement detection
• Finite-Time Disentanglement via Spontaneous Emission
• Non-Markovian effects on the dynamics of entanglement
• Unconditional quantum teleportation between distant solid-state qubits
• Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
• How to Enhance Dephasing Time in Superconducting Qubits
• Scalable quantum register based on coupled electron spins in a room temperature solid
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Nuclear spin physics in quantum dots: an optical investigation
• Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Entanglement dynamics of two independent qubits in environments with and without memory
• Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots
• Enhancing the Coherence of a Spin Qubit by Operating it as a Feedback Loop That Controls its Nuclear Spin Bath
• Ultrafast optical control of entanglement between two quantum dot spins
• Spin-echo of a single electron spin in a quantum dot
• Quantum many-body theory of qubit decoherence in a finite-size spin bath
• Suppressing qubit dephasing using real-time Hamiltonian estimation
• Singlet-triplet decoherence due to nuclear spins in a double quantum dot
• Electron Spin Dephasing due to Hyperfine Interactions with a Nuclear Spin Bath
• Pure quantum dephasing of a solid state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions
• Ultra-long distance interaction between spin qubits
• Nuclear Spins in Nanostructures
• Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling
• Quantum computing by optical control of electron spins
• Measurement of Temporal Correlations of the Overhauser Field in a Double Quantum Dot
• Nonperturbative master equation solution of central spin dephasing dynamics
• On experimental procedures for entanglement verification
• Conditional operation of a spin qubit
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Exponential decay in a spin bath
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Electron spin as a spectrometer of nuclear spin noise and other fluctuations
• Spatial adiabatic passage in a realistic triple well structure
• Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath
• Quantum versus classical hyperfine-induced dynamics in a quantum dot
• Spin echo decay at low magnetic fields in a nuclear spin bath
• Decoherence of coupled electron spins via nuclear spin dynamics in quantum dots
• Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach
• Decay of Entanglement for Solid-State Qubits
• The decay of quantum correlations between quantum dot spin qubits and the characteristics of its magnetic field dependence

Cited by in corpus (10)

• Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof
• Environmental noise effects on entanglement fidelity of exchange-coupled semiconductor spin qubits
• Ultimate entanglement robustness of two-qubit states against general local noises
• Theory of box-model hyperfine couplings and transport signatures of long-range nuclear-spin coherence in a quantum-dot spin valve
• Performance of quantum registers in diamond in the presence of spin impurities
• Qubit-environment entanglement outside of pure decoherence: hyperfine interaction
• Simulating decoherence of two coupled spins using the generalized cluster correlation expansion
• Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots
• Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles
• Retardation of entanglement decay of two spin qubits by quantum measurements