A new kind of geometric phases in open quantum systems and higher gauge theory

Viennot, David; Lages, José

doi:10.1088/1751-8113/44/36/365301

Cited by 11 publications

(55 citation statements)

References 42 publications

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“…, the operator valued geometric phases found in the present paper coincides with the definition introduced in [17] which is a generalization of the geometric phases introduced in [13,14,15,16].…”

Section: Discussion About the Operator-valued Phasessupporting

confidence: 79%

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Viennot¹,

Aubourg²

2014

J. Phys. A: Math. Theor.

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Abstract. We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered component is described by adiabatic transport formulae exhibiting operator-valued geometric and dynamical phases. The present results can be used to study the quantum control of the dynamics of qubits and of open quantum systems where the two components are the system and its environment. We treat two examples, the control of an atomic qubit interacting with another one and the control of a spin in the middle of a Heisenberg spin chain.

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Section: Discussion About the Operator-valued Phasessupporting

confidence: 79%

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Viennot¹,

Aubourg²

2014

J. Phys. A: Math. Theor.

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“…This suggests a possible connection between the localized qubit theory with matrix models and then with supergravity (due to the correspondance between the two theories [13]). Moreover, non-commutative eigenequations as Z i ⊗ σ i |Λ = z i σ i |Λ appear also in the adiabatic theory of entangled quantum systems and their operator valued geometric phases [14,15]. It could be then possible that the connection between the localized qubit theory and D-brane matrix models enlighten the qubit/black-hole correspondence [16,17], where some properties of STU black holes are in correspondence with the entanglement states of several qubits.…”

Section: Adiabatic Approximationmentioning

confidence: 99%

Adiabatic transport of qubits around a black hole

Viennot

Moro

2017

Class. Quantum Grav.

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We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a single framework. The quantum decoherence induced by the black hole on the qubit is analysed in this framework (the role of the dynamical and geometric phases in this decoherence is treated), especially for the quantum teleportation protocol when one qubit falls to the event horizon. A simple formula to compute the fidelity of the teleportation is derived. The case of a Schwarzschild black hole is analysed.

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“…Singularities and entropic strings of these fields indicate these regions of M . The generator of the C * -geometric phase is solution of the equation [6] dρ a = A a ρ a + ρ a A † a…”

Section: 12mentioning

confidence: 99%

“…We want a geometric characterization of the defects induced by the entanglement. Recently, we have proposed a generalization of the geometric phase concept for open and composite quantum systems [6,7]. This geometric phase takes its values in the C * -algebra of the operators of the quantum system.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic quantum control hampered by entanglement

Viennot¹

2014

J. Phys. A: Math. Theor.

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Abstract. We study the defects in adiabatic control of a quantum system caused by the entanglement of the system with its environment. Such defects can be assimilated to decoherence processes due to perturbative couplings between the system and the environment. To analyse these effects, we propose a geometric approach, based on a field theory on the control manifold issued from the higher gauge theory associated with the C * -geometric phases. We study a visualization method to analyse the defects of the adiabatic control based on the drawing of the field strengths of the gauge theory. To illustrate the present methodology we consider the example of the atomic STIRAP (stimulated Raman adiabatic passage) where the controlled atom is entangled with another atom. We study the robustness of the STIRAP effect when the controlled atom is entangled with another one.

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A new kind of geometric phases in open quantum systems and higher gauge theory

Cited by 11 publications

References 42 publications

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Adiabatic transport of qubits around a black hole

Adiabatic quantum control hampered by entanglement

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