Robustness of quantum Markov chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.Comment: 14 pages, no figures; not for the feeble-minde

Decoherence Strength of Multiple Non-Markovian Environments

It is known that one can characterize the decoherence strength of a Markovian environment by the product of its temperature and induced damping, and order the decoherence strength of multiple environments by this quantity. We show that for non-Markovian environments in the weak coupling regime there also exists a natural (albeit partial) ordering of environment-induced irreversibility within a perturbative treatment. This measure can be applied to both low-temperature and non-equilibrium environments.Comment: 6 pages, 1 figure, v3 included figure, appendix, and clarification of result

Information capacity of quantum observable

In this paper we consider the classical capacities of quantum-classical channels corresponding to measurement of observables. Special attention is paid to the case of continuous observables. We give the formulas for unassisted and entanglement-assisted classical capacities $C,C_{ea}$ and consider some explicitly solvable cases which give simple examples of entanglement-breaking channels with $C<C_{ea}.$ We also elaborate on the ensemble-observable duality to show that $C_{ea}$ for the measurement channel is related to the $\chi$-quantity for the dual ensemble in the same way as $C$ is related to the accessible information. This provides both accessible information and the $\chi$-quantity for the quantum ensembles dual to our examples.Comment: 13 pages. New section and references are added concerning the ensemble-observable dualit

A γ-β frequency transition generated by inter-areal communication in the hippocampus in vitro

Gamma oscillations are generated in area CA3 of the hippocampus both in vitro and in vivo (Fisahn et al., 1998; Csicsvari et al., 2003). Here we present experimental and network simulation data to elucidate the mechanism of the generation of CA3-driven gamma and beta oscillations in area CA1. (1) The frequency of area CA1 output generated by gamma input from area CA3 was dependent on the degree of recruitment of CA1 principal cells. Passive involvement of area CA1 principal cells resulted in a gamma frequency oscillation. Active involvement of CA1 principal cells transformed this gamma oscillation into one at beta frequencies. (2) This beta oscillation in area CA1 was dependent on CA1 recurrent excitation. (3) It was also dependent on the temporal relationship between feedforward excitation of CA1 interneurons (by CA3 output) and feedback excitation of CA1 interneurons (by CA1 output). That is, the network beta oscillation in area CA1 depended on doublet firing of certain interneurons driven by area CA3. (4) The interneuron doublet rate during beta corresponded to whether or not dendrites are oriented horizontally or vertically: Interneurons with vertically oriented dendrites (eg. basket cells and - to a lesser extent - bistratified cells, all receiving input from CA3) fired considerably more doublets than interneurons with horizontally oriented dendrites (horizontal alveus cells or olm cells) which are not contacted by area CA3 and hardly ever fired doublets during beta. Taken together the findings demonstrate that different interneurons can serve different purposes during a given network oscillation, that single interneuron subtypes can mediate multiple network frequencies, and that the frequency of output from a cortical region serves to signal the degree of principal cell recruitment

A γ-β frequency transition generated by inter-areal communication in the hippocampus in vitro

Gamma oscillations are generated in area CA3 of the hippocampus both in vitro and in vivo (Fisahn et al., 1998; Csicsvari et al., 2003). Here we present experimental and network simulation data to elucidate the mechanism of the generation of CA3-driven gamma and beta oscillations in area CA1. (1) The frequency of area CA1 output generated by gamma input from area CA3 was dependent on the degree of recruitment of CA1 principal cells. Passive involvement of area CA1 principal cells resulted in a gamma frequency oscillation. Active involvement of CA1 principal cells transformed this gamma oscillation into one at beta frequencies. (2) This beta oscillation in area CA1 was dependent on CA1 recurrent excitation. (3) It was also dependent on the temporal relationship between feedforward excitation of CA1 interneurons (by CA3 output) and feedback excitation of CA1 interneurons (by CA1 output). That is, the network beta oscillation in area CA1 depended on doublet firing of certain interneurons driven by area CA3. (4) The interneuron doublet rate during beta corresponded to whether or not dendrites are oriented horizontally or vertically: Interneurons with vertically oriented dendrites (eg. basket cells and - to a lesser extent - bistratified cells, all receiving input from CA3) fired considerably more doublets than interneurons with horizontally oriented dendrites (horizontal alveus cells or olm cells) which are not contacted by area CA3 and hardly ever fired doublets during beta. Taken together the findings demonstrate that different interneurons can serve different purposes during a given network oscillation, that single interneuron subtypes can mediate multiple network frequencies, and that the frequency of output from a cortical region serves to signal the degree of principal cell recruitment

Robustness of Decoherence-Free Subspaces for Quantum Computation

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.Comment: 16 pages, no figures. Several changes, including a clarification of the derivation of the Lindblad equation from the operator sum representation. To appear in Phys. Rev

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

An African Approach for Risk Reduction of Soil Contaminated by Obsolete Pesticides

Since the 1950s, large amounts of pesticides were shipped to Africa for locust control, but did not arrive at the proper place or proper time thereby rendering them obsolete. Stockpiles of these pesticides have created a serious problem and The Africa Stockpiles Programme (ASP), launched by FAO, is designed to rid Africa of stockpiles and to dispose of them in an environmentally sound manner (ASP, 2009). From July to August 2007, an investigation mission was organized by FAO pesticide management programme, in collaboration with Wageningen University and Research Centre and the relevant national counterpart institutions of the Ministries of Agriculture and the Ministries of Environment in Mali and Mauritania. During the investigation, three sites in Mali and three sites in Mauretania were visited in the summer of 2007. High concentrations of pesticides were found in soils on the stockpiles. From a riskbased point of view, contaminations are only a risk if they are or may become available. Based on the results obtained and results of analysis of the samples taken, risk reduction proposals have been developed. All proposals are based on stimulation of the possibilities of biological degradation of the pesticides in combination with isolation and preventing rain water from transporting the pesticides. The results were discussed in May 2008 and the first implementation was started in Molodo (Mali) in July 2008

Locality and Causality in Hidden Variables Models of Quantum Theory

Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's (and similar) hidden variables models can be extended to an important class of generalized observables. Finally a result of Fine on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.Comment: revised version, 21 pages, submitted to Physical Review