Models of decoherence with negative dephasing rate

We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system–environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of 'non-Markovianity' will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system–environment correlations. Depending on the initial purity of the qubit state, these system–environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system–environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and 'non-Markovianity'.We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system–environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of 'non-Markovianity' will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system–environment correlations. Depending on the initial purity of the qubit state, these system–environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system–environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and 'non-Markovianity'.

arXiv:1202.4280Journal of Physics B Atomic Molecular and Optical PhysicsJul 30, 201240 citations

System-environment correlations for dephasing two-qubit states coupled to thermal baths

Ana C. S. Costa, Marcus W. Beims, Walter T. Strunz

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature ${T}_{\mathrm{crit}}$ . On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to ${T}_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature ${T}_{\mathrm{crit}}$. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to ${T}_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.

arXiv:1605.04154Physical Review AMay 12, 201615 citations

Constant quantum correlations in Markovian and non-Markovian environments

Laura Mazzola, Jyrki Piilo, Sabrina Maniscalco

"We investigate the dynamics of quantum correlation of two qubits under local dephasing channels. We demonstrate the constancy of quantum correlation for long interval of times despite the detrimental effects of the environments. The natural protection of quantum correlation is accompanied by losses of classical correlation. At a sharp time, quantum and classical correlations exchange their roles: quantum corre- lation starts to decay while classical correlations become constant. We have called this phenomenon “sudden transition between classical and quantum decoherence” [Physical Review Letters 104, 200401 (2010)] . Such a dynamical feature is not the result of the Markovian approximation, but it appears in a much richer way also in the non-Markovian scenario.""We investigate the dynamics of quantum correlation of two qubits under local dephasing channels. We demonstrate the constancy of quantum correlation for long interval of times despite the detrimental effects of the environments. The natural protection of quantum correlation is accompanied by losses of classical correlation. At a sharp time, quantum and classical correlations exchange their roles: quantum corre- lation starts to decay while classical correlations become constant. We have called this phenomenon “sudden transition between classical and quantum decoherence” [Physical Review Letters 104, 200401 (2010)] . Such a dynamical feature is not the result of the Markovian approximation, but it appears in a much richer way also in the non-Markovian scenario."

Revista Mexicana de FísicaJan 1, 20111 citation

Non-Markovianity with Pure Dephasing Environment and Quantum Information Processing with Rydberg Atoms

Alexandre Cesa

In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.

Sep 16, 20190 citations

Quantum oscillations in the spin-boson model: reduced visibility from non-Markovian effects and initial entanglement

Frank K. Wilhelm

The loss of coherence of quantum oscillations is of fundamental interest as well as of practical importance in quantum computing. In solid-state experiments the oscillations show, next to the familiar exponential decay on time scales T 1/2 , an overall loss of amplitude. We solve the spin-boson model for a large class of initial conditions without the Markov approximation at the pure dephasing point. It is shown that a loss of visibility occurs in the form of a fast initial drop for factorized initial conditions and an overall reduction for entangled initial conditions. This loss of amplitude is distinct from T 2 -decoherence with the difference being most drastic for environments with real or pseudo-gaps. This result is explained by bandwidth effects in quantum noise as well as in terms of higher order phase-breaking processes. For several experiments, such gapped environments are identified. We confirm that this physics is valid beyond the pure dephasing point.The loss of coherence of quantum oscillations is of fundamental interest as well as of practical importance in quantum computing. In solid-state experiments the oscillations show, next to the familiar exponential decay on time scales T 1/2 , an overall loss of amplitude. We solve the spin-boson model for a large class of initial conditions without the Markov approximation at the pure dephasing point. It is shown that a loss of visibility occurs in the form of a fast initial drop for factorized initial conditions and an overall reduction for entangled initial conditions. This loss of amplitude is distinct from T 2 -decoherence with the difference being most drastic for environments with real or pseudo-gaps. This result is explained by bandwidth effects in quantum noise as well as in terms of higher order phase-breaking processes. For several experiments, such gapped environments are identified. We confirm that this physics is valid beyond the pure dephasing point.

arXiv:cond-mat/0507526New Journal of PhysicsNov 20, 200812 citations

Analytical results for the quantum non-Markovianity of spin ensembles undergoing pure dephasing dynamics

R. Dubertrand, Alexandre Cesa, John Martin

We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo et al. [Phys. Rev. A 88, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment's size goes to infinity. In this limit and for finite-size systems, we find that the Markovian character of the system's dynamics crucially depends on the range of the interactions. We also show that when the system and its environment are initially in a product state, the appearance of non-Markovianity is independent of the entanglement generation between the system and its environment.We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo et al. [Phys. Rev. A 88, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment's size goes to infinity. In this limit and for finite-size systems, we find that the Markovian character of the system's dynamics crucially depends on the range of the interactions. We also show that when the system and its environment are initially in a product state, the appearance of non-Markovianity is independent of the entanglement generation between the system and its environment.

arXiv:1803.04519Physical Review AJun 26, 20181 citation

X

state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature

{T}_{\mathrm{crit}}

. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to

{T}_{\mathrm{crit}}

the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.