Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof

Abstract

We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In case of the discord with respect to the qubit, a vast majority of separable states qubit-environment is discordant, but in specific situations zero-discord states are possible. This is conceptually important since there is a connection between the discordance with respect to a given subsystem and the possibility of describing the evolution of this subsystem using completely positive maps. Finally, we use the formalism to find an exemplary evolution of an entangled state of two qubits that is completely positive, occurs solely due to interaction of only one of the qubits with its environment (so one could guess that it corresponds to a local operation, since it is local in a physical sense), but which nevertheless causes the enhancement of entanglement between the qubits. While this simply means that the considered evolution is completely positive, but does not belong to LOCC, it shows how much caution has to be exercised when identifying evolution channels that belong to that class.

10 pages, 1 figure

References in corpus (16)

• Necessary and sufficient condition for non-zero quantum discord
• 14-qubit entanglement: creation and coherence
• Universal dynamical decoupling of a single solid-state spin from a spin bath
• Sudden Death of Entanglement: Classical Noise Effects
• Completely Positive Maps and Classical Correlations
• Pure quantum dephasing of a solid state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions
• Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins
• Anomalous decoherence effect in a quantum bath
• Separable Operations on Pure States
• Nonlocal Entanglement Transformations Achievable by Separable Operations
• "Which path" decoherence in quantum dot experiments
• Analytical progress on symmetric geometric discord: Measurement-based upper bounds
• Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
• The decay of quantum correlations between quantum dot spin qubits and the characteristics of its magnetic field dependence

Cited by in corpus (17)

• A scheme for direct detection of qubit-environment entanglement generated during qubit pure dephasing
• Noise representations of open system dynamics
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Qubit-environment entanglement generation and the spin echo
• A measure of qubit environment entanglement for pure dephasing evolutions
• Detection of entanglement during pure dephasing evolutions for systems and environments of any size
• Transfer and teleportation of system-environment entanglement
• Qubit-environment entanglement outside of pure decoherence: hyperfine interaction
• A glimpse of objectivity in bipartite systems for non-entangling pure dephasing evolutions
• Appearance of objectivity for NV centers interacting with dynamically polarized nuclear environment
• Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system
• Memory effects in multipartite systems coupled by non-diagonal dephasing mechanisms
• Qubit-environment entanglement in time-dependent pure dephasing
• Superclassical non-Markovian open quantum dynamics
• A signature of quantumness in pure decoherence control
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• Experimental protocol for qubit-environment entanglement detection