We consider the coupling of a qubit in a pure state to an environment in an arbitrary state, and characterize the possibility of qubit-environment entanglement generation during the evolution of the joint system, that leads to pure dephasing of the qubit. We give a simple necessary and sufficient condition on the initial density matrix of the environment together with the properties of the interaction, for appearance of qubit-environment entanglement. Any entanglement created turns out to be detectable by the Peres-Horodecki criterion. Furthermore, we show that for a large family of initial environmental states, the appearance of nonzero entanglement with the environment is necessarily accompanied by a change in the state of the environment (i.e. by the back-action of the qubit). When a quantum system, a qubit (Q) in the context of this paper, is coupled to an environment (E), an initial pure state of the qubit evolves into a mixed state. It is widely recognized that there is an intimate relation between this process of decoherence [1, 2] and creation of qubit-environment entanglement (QEE). A precise statement can be made for E initialized in a pure state: the establishment of QEE is then equivalent to the reduction of purity of the reduced density matrix of Q. However, in the case of an initial mixed state of E, the situation is more complicated: the state of Q can lose its purity while no QEE is established [3]. This should not be surprising, since QEE should be associated with decoherence, understood as a process in which information is transferred from Q to E (i.e. E is in some sense "measuring" Q), not with the bare fact that the state of Q is becoming mixed. The latter can happen when there is no influence of Q on E. For example, when the self-HamiltonianĤ E of E commutes with the qubit-environment interactionV QE , and when the initial state of E fulfillsρ E (0) = f (Ĥ E ) (e.g. it is a thermal state determined byĤ E ), there is no back-action of Q on E, while E is simply a source of random, classical, and quasi-static fields acting on Q [4][5][6][7]. In this case of so-called random unitary (RU) evolution, the purity of Q decays while no QEE is established.A natural question to ask is whether the RU case is the only one for which QEE does not accompany the loss of purity of Q. While specific kinds of environments and qubit-environment couplings were investigated in this context (e.g. quantum Brownian motion [3,8] or pure dephasing due to a bath of noninteracting bosons [9]), the general answer to this question seems to be lacking. This is to a large degree caused by the fact that quantification (or even checking for presence) of QEE is a very hard problem when mixed states of the total system are considered, and when the dimension of Hilbert space of E is larger than 3 [10-13]. The existence of bound entanglemet [14,15] (which is not detected by the Peres-Horodecki criterion [16,17] of negativity of a partially transposed matrix of the total system) severely hampers the task of general understanding of Q...

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We study single-qubit gates performed via stimulated Raman adiabatic passage (STIRAP) on a spin qubit implemented in a quantum dot system in the presence of phonons. We analyze the interplay of various kinds of errors resulting from the carrier-phonon interaction (including also the effects of spin-orbit coupling) as well as from quantum jumps related to nonadiabaticity and calculate the fidelity as a function of the pulse parameters. We give quantitative estimates for an InAs/GaAs system and identify the parameter values for which the error is considerably minimized, even to values below 10 −4 per operation.

An evolution between a system and its environment which leads to pure dephasing of the system may either be a result of entanglement building up between the system and the environment or not (the second option is only possible for initially mixed environmental states). We find a way of distinguishing between an entangling and non-entangling evolutions for systems which are larger than a single qubit. The generalization of the single qubit separability criterion to larger systems is not sufficient to make this distinction (it constitutes a necessary condition of separability). A set of additional conditions for the operators describing the evolution of the environment depending on the state of the system is required. We find that the commutation of these environmental operators with the initial state of the environment does not guarantee separability, products of the operators need to commute among themselves for a pure dephasing evolution not to be accompanied by system-environment entanglement generation. This is a qualitative difference with respect to the single-qubit case, since it allows for a system to entangle with an initially completely mixed environment.PACS numbers:

We study the effect of pure dephasing on the entanglement of a pair of two-level subsystems (qubits). We show that partial dephasing induced by a super-Ohmic reservoir, corresponding to well-established properties of confined charge states and phonons in semiconductors, may lead to complete disentanglement. We show also that the disentanglement effect increases with growing distance between the two subsystems.Comment: Final, considerably extended version, 6 pages, 4 figure

In the published version of our paper, the numerical coefficients in Eq. ͑7͒ are incorrect. This equation should readMoreover, the fifth geometrical factor ͑at the end of Sec. III͒ should be M 2h,t1 ͑͒ = M −2h,t1 ͑͒ = sin 2 . The values plotted in Fig. 1 were also computed incorrectly. When these errors are corrected, the values in the main panel of Fig. 1 must be reduced by a factor of about 30 and the values in the inset to this figure must be reduced by a factor of 2. Also the dynamics of sequential transitions ͑Fig. 3͒ becomes correspondingly slower.The main conclusions of our paper remain valid: For the chosen values of the parameters the transition to dark states is the fastest spin decoherence channel. Its rate exceeds that corresponding to the direct transition between bright states by a factor of about 7 for the fine structure splitting ␦ = 0.1 meV and by a factor of about 28 for ␦ = 0.05 meV. Moreover, the dominant role in both processes is played by transverse acoustic phonons. They contribute about 96% and 98% of the total transition rate for the relaxation to dark states and between bright states, respectively.After the publication of our paper we have learned about an earlier work on a similar subject. 1 In that paper, transitions to dark and bright states were studied for a system in a magnetic field but only at zero temperature and only with longitudinal acoustic phonons included.

We analyze and interpret recent optical experiments with semiconductor quantum dots. We derive a quantitative relation between the amount of information transferred into the environment and the optical polarization that may be observed in a spectroscopy experiment.

We show that singlet-triplet superpositions of two-electron spin states in a double quantum dot undergo a phonon-induced pure dephasing which relies only on the tunnel coupling between the dots and on the Pauli exclusion principle. As such, this dephasing process is independent of spin-orbit coupling or hyperfine interactions. The physical mechanism behind the dephasing is elastic phonon scattering, which persists to much lower temperatures than real phonon-induced transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs gate-defined double quantum dot yield micro-second dephasing times at sub-Kelvin temperatures, which is consistent with experimental observations.