Optimality of programmable quantum measurements

We prove that for a programmable measurement device that approximates every POVM with an error $\le \delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta}$. In the case of qubits we can improve the general result by showing a linear growth. This proves the optimality of the programmable measurement devices recently designed in [G. M. D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)]

Compression and R-wave detection of ECG/VCG data

Application of information theory to eliminate redundant part of electrocardiogram or vectorcardiogram is described. Operation of medical equipment to obtain three dimensional study of patient is discussed. Use of fast Fourier transform to accomplish data compression is explained

Typical entanglement of stabilizer states

How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code. Finally, we show that typically very few GHZ states can be extracted from a random multipartite stabilizer state via local unitary operations. Our main tool is a new concentration inequality which bounds deviations from the mean of random variables which are naturally defined on the Clifford group.Comment: Final version, to appear in PRA. 11 pages, 1 figur

Quantum Phase Transitions in the Itinerant Ferromagnet ZrZn2_2

We report a study of the ferromagnetism of ZrZn$_{2}$, the most promising material to exhibit ferromagnetic quantum criticality, at low temperatures $T$ as function of pressure $p$. We find that the ordered ferromagnetic moment disappears discontinuously at $p_c$=16.5 kbar. Thus a tricritical point separates a line of first order ferromagnetic transitions from second order (continuous) transitions at higher temperature. We also identify two lines of transitions of the magnetisation isotherms up to 12 T in the $p-T$ plane where the derivative of the magnetization changes rapidly. These quantum phase transitions (QPT) establish a high sensitivity to local minima in the free energy in ZrZn$_{2}$, thus strongly suggesting that QPT in itinerant ferromagnets are always first order

Quantum information reclaiming after amplitude damping

We investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular we address the question of optimal measurement on the environment to perform the best possible correction on two and three dimensional quantum systems. Depending on the dimension we show that the entanglement fidelity (the measure quantifying the correction performance) is or is not the same for all possible measurements and uncover the optimal measurement leading to the maximum entanglement fidelity

Quantum states representing perfectly secure bits are always distillable

It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on distillable cryptographic key in bipartite scenario.Comment: RevTeX, 5 pages, published versio

Entropy and Entanglement in Quantum Ground States

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.Comment: 7 pages, no figure

Fluvial Sinuous Ridges of the Morrison Formation, USA: Meandering, Scarp Retreat, and Implications for Mars

Sinuous ridges have been interpreted as evidence for ancient rivers on Mars, but relating ridge geometry to paleo‐hydraulics remains uncertain. Three analog ridge systems from the Morrison Formation, Utah, are composed of sandstone caprocks, up to 50 m wide and 8 m thick, atop mudstone flanks. Ridge caprocks have narrowed significantly compared to sandstone bodies preserved in outcrop, consistent with a new ridge‐erosion model that can be used to estimate original sandstone‐body extent. Ridge networks represent caprocks intersecting at distinct stratigraphic levels, rather than a preserved channel network. Caprocks are interpreted as amalgamated channel belts, rather than inverted channels, with dune and bar cross stratification that was used to reconstruct paleo‐channel dimensions. Curvilinear features on ridge tops are outcropping lateral accretion sets (LAS) from point bars and indicate meandering. We found that caprock thickness scales with paleo‐channel depth and LAS curvature scales with paleo‐channel width. Application of these relations to a ridge in Aeolis Dorsa, Mars, yielded consistent water discharge estimates (310–1,800 m³/s). In contrast, using ridge width or ridge radius of curvature as paleo‐channel proxies overestimated discharge by a factor of 30–500. In addition, the ridge‐erosion model suggests that scarp retreat may be less efficient on Mars, resulting in taller and wider ridges, with more intact caprocks. Altogether, our results support the hypothesis that ridges are exhumed channel belts and floodplain deposits implying long‐lived fluvial activity recorded within a depositional basin

Fluvial Sinuous Ridges of the Morrison Formation, USA: Meandering, Scarp Retreat, and Implications for Mars

Sinuous ridges have been interpreted as evidence for ancient rivers on Mars, but relating ridge geometry to paleo‐hydraulics remains uncertain. Three analog ridge systems from the Morrison Formation, Utah, are composed of sandstone caprocks, up to 50 m wide and 8 m thick, atop mudstone flanks. Ridge caprocks have narrowed significantly compared to sandstone bodies preserved in outcrop, consistent with a new ridge‐erosion model that can be used to estimate original sandstone‐body extent. Ridge networks represent caprocks intersecting at distinct stratigraphic levels, rather than a preserved channel network. Caprocks are interpreted as amalgamated channel belts, rather than inverted channels, with dune and bar cross stratification that was used to reconstruct paleo‐channel dimensions. Curvilinear features on ridge tops are outcropping lateral accretion sets (LAS) from point bars and indicate meandering. We found that caprock thickness scales with paleo‐channel depth and LAS curvature scales with paleo‐channel width. Application of these relations to a ridge in Aeolis Dorsa, Mars, yielded consistent water discharge estimates (310–1,800 m³/s). In contrast, using ridge width or ridge radius of curvature as paleo‐channel proxies overestimated discharge by a factor of 30–500. In addition, the ridge‐erosion model suggests that scarp retreat may be less efficient on Mars, resulting in taller and wider ridges, with more intact caprocks. Altogether, our results support the hypothesis that ridges are exhumed channel belts and floodplain deposits implying long‐lived fluvial activity recorded within a depositional basin