A. K. Rajagopal

Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory

Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. [Nature Phys. 6, 659 (2010)] have shown that the lower bound on the uncertainties of the measurement outcomes depends on the correlations between the observed system and an observer who possesses a quantum memory. If the system is maximally entangled with its memory, the outcomes of two incompatible measurements made on the system can be predicted precisely. Here, we obtain an uncertainty relation that tightens the lower bound of Berta et al. by incorporating an additional term that depends on the quantum discord and the classical correlations of the joint state of the observed system and the quantum memory. We discuss several examples of states for which our lower bound is tighter than the bound of Berta et al. On the application side, we discuss the relevance of our inequality for the security of quantum key distribution and show that it can be used to provide bounds on the distillable common randomness and the entanglement of formation of bipartite quantum states.

Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity

Dynamical

Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms

A

Generalized information theoretic measure to discern the quantumness of correlations.

and

Characterizing Multiparticle Entanglement in Symmetric N-Qubit States via Negativity of Covariance Matrices

B

Macrorealism from entropic Leggett-Garg inequalities

maps have been employed extensively by Sudarshan and co-workers to investigate open-system evolution of quantum systems. A canonical structure of the

Monogamy of quantum correlations in three-qubit pure states

A

Majorana representation of symmetric multiqubit states

map is introduced here. It is shown that this canonical

From the quantum relative Tsallis entropy to its conditional form: Separability criterion beyond local and global spectra

A

Constraints on the uncertainties of entangled symmetric qubits

map enables us to investigate whether the dynamics is completely positive (CP) or not completely positive (NCP) in an elegant way and, hence, it subsumes the basic results on open-system dynamics. Identifying memory effects in open-system evolution is gaining increasing importance recently and, here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization\char22{}though not related directly\char22{}to the fidelity difference criterion proposed recently. Three typical examples of open-system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics\char22{}which corresponds to a NCP dynamical map\char22{}are investigated by employing both the relative entropy difference and fidelity difference tests of non-Markovianity. The two-qubit initial states are chosen to be (i) a pure entangled state, (ii) the Werner state, which exemplifies both entangled and separable states of qubits, depending on a real parameter, and (iii) a separable mixed state. Both the relative entropy and fidelity criteria offer a nice display of how non-Markovianity manifests itself in all three examples.