Classification of nonproduct states with maximum stabilizer dimension

Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups of the group of local unitary transformations are precisely the generalized n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents, for n greater than or equal to 3 but not equal to 4. We characterize the Lie algebra of the stabilizer subgroup for these states. For n=4, there is an additional maximal stabilizer subalgebra, not local unitary equivalent to the former. We give a canonical form for states with this stabilizer as well.Comment: 6 pages, version 3 has a typographical correction in the displayed equation just after numbered equation (2), and other minor correction

An Expert Survey of Information Needs for Ohio River Sport and Commercial Fishes

Author Institution: Department of Fisheries and Wildlife Sciences, Virginia Polytechnic Institute and State UniversityForty-eight Ohio River fishery managers from six states were surveyed to assess the relative importance of sport and commercial fisheries data gaps on the Ohio River. Twenty-two experts responded to the complex survey, which asked respondents to judge the need for 40 data types for each of seven taxa. Among taxa, information needs were highest for white bass and hybrids (Morone spp.) and buffalofishes (Ictiobus spp.), and lowest for bass/sunfish (Micropterus/Lepomis spp.) and common carp (Cyprinus carpio). Among data types, information needs were highest for natural and fishing mortality rates, and lowest for fecundity. Among life stages, information needs were highest for larval fishes, and lowest for adults during spawning season and summer. Expert opinions on information needs can be used to direct research and monitoring studies to highest priority needs and to avoid duplicative studies

Classification of n-qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Ancilla models for quantum operations: For what unitaries does the ancilla state have to be physical?

Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary operator, acting on the system and the ancilla. Here we study the properties such a unitary operator must have in order to force the choice of a physical- that is, positive-state for the ancilla if the end result is to be a physical-that is, completely positive-evolution of the system.Comment: Quantum Information Processing, (2012

Immunosuppressants and risk of Parkinson disease

We performed a population-based case-control study of United States Medicare beneficiaries age 60-90 in 2009 with prescription data (48,295 incident Parkinson disease cases and 52,324 controls) to examine the risk of Parkinson disease in relation to use of immunosuppressants. Inosine monophosphate dehydrogenase inhibitors (relative risk = 0.64; 95% confidence interval 0.51-0.79) and corticosteroids (relative risk = 0.80; 95% confidence interval 0.77-0.83) were both associated with a lower risk of Parkinson disease. Inverse associations for both remained after applying a 12-month exposure lag. Overall, this study provides evidence that use of corticosteroids and inosine monophosphate dehydrogenase inhibitors might lower the risk of Parkinson disease

Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group

We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords connecting pairs of points on a circle, and give a criterion for when the stabilizer is precisely the diagonal subgroup and not larger. This investigation is part of a larger program to partially classify entanglement type (local unitary equivalence class) via analysis of stabilizer structure.Comment: 4 pages, 3 figures. Version 2 has numerous small changes and correction

Deterministic and Unambiguous Dense Coding

Optimal dense coding using a partially-entangled pure state of Schmidt rank $\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability $\tau_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-\tau_x$) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For $\bar D\leq D$ a bound is obtained for $L_d$ in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. For $\bar D > D$ it is shown that $L_d$ is strictly less than $D^2$ unless $\bar D$ is an integer multiple of $D$, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for $\bar D \leq D$, assuming $\tau_x>0$ for a set of $\bar D D$ messages, and a bound is obtained for the average \lgl1/\tau\rgl. A bound on the average \lgl\tau\rgl requires an additional assumption of encoding by isometries (unitaries when $\bar D=D$) that are orthogonal for different messages. Both bounds are saturated when $\tau_x$ is a constant independent of $x$, by a protocol based on one-shot entanglement concentration. For $\bar D > D$ it is shown that (at least) $D^2$ messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.Comment: Short new section VII added. Latex 23 pages, 1 PSTricks figure in tex

Local cloning of entangled states

We investigate the conditions under which a set \SC of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in \SC must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set \SC can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with non-vanishing entanglement. In both of these cases, a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary "shift" operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher dimensional systems, we find that the resource state must be strictly more entangled than the states in \SC. All of our necessary conditions for separable operations are also necessary conditions for LOCC, since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.Comment: REVTEX 15 pages, 1 figure, minor modifications. Same as the published version. Any comments are welcome

Entanglement of bosonic modes of nonplanar molecules

Entanglement of bosonic modes of material oscillators is studied in the context of two bilinearly coupled, nonlinear oscillators. These oscillators are realizable in the vibrational-cum-bending motions of C-H bonds in dihalomethanes. The bilinear coupling gives rise to invariant subspaces in the Hilbert space of the two oscillators. The number of separable states in any invariant subspace is one more than the dimension of the space. The dynamics of the oscillators when the initial state belongs to an invariant subspace is studied. In particular, the dynamics of the system when the initial state is such that the total energy is concentrated in one of the modes is studied and compared with the evolution of the system when the initial state is such wherein the modes share the total energy. The dynamics of quantities such as entropy, mean of number of quanta in the two modes and variances in the quadratures of the two modes are studied. Possibility of generating maximally entangled states is indicated.Comment: 21 pages, 6 figure