Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change

Dynamical stability of entanglement between spin ensembles

We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be very useful to generate and detect macroscopic entanglement in a common noisy environment and even a stable macroscopic memory.Comment: 4 pages, 1 figur

Solutions of the Ginsparg-Wilson Relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13

Physical Purification of Quantum States

We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a pure state in a higher-dimensional Hilbert space, the reduced density matrix of which is identical to the original state. We characterize all sets of mixed quantum states, for which perfect purification is possible. Surprisingly, some sets of two non-commuting states are among them. Furthermore, we investigate the possibility of performing an imperfect purification.Comment: 5 pages, 1 figure; published versio

Quantum Entanglement Capacity with Classical Feedback

For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback ($E_B$), and we show that this quantity lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication ($Q_2$) and the quantum capacity with classical feedback ($Q_B$) - are widely conjectured to be different: there exists quantum discrete memoryless channel for which $Q_2>Q_B$. We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly-defined quantity of the quantum depolarizing channel, and illustrate with Cat (repetition) code and Shor code. We contrast the present notion with entanglement purification protocols by showing that whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned Cat code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any $E_B$ protocols. We then apply this formula to the $E_B$ protocols that we discuss to obtain new lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel

Quantum superadditivity in linear optics networks: sending bits via multiple access Gaussian channels

We study classical capacity regions of quantum Gaussian multiple access channels (MAC). In classical variants of such channels, whilst some capacity superadditivity-type effects such as the so called {\it water filling effect} may be achieved, a fundamental classical additivity law can still be identified, {\it viz.} adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. Here, we show that quantum resources allows violation of this law, by providing two illustrative schemes of experimentally feasible Gaussian MACs.Comment: 4 pages, 2 figure

MAGIICAT V. Orientation of Outflows and Accretion Determine the Kinematics and Column Densities of the Circumgalactic Medium

We investigate the dependence of gas kinematics and column densities in the MgII-absorbing circumgalactic medium on galaxy color, azimuthal angle, and inclination to trace baryon cycle processes. Our sample of 30 foreground isolated galaxies at $0.3<z_{\rm gal}<1.0$, imaged with the Hubble Space Telescope, are probed by background quasars within a projected distance of $20<D<110$ kpc. From the high-resolution ($\Delta v\simeq 6.6$ km s$^{-1}$) quasar spectra, we quantify the extent of the absorber velocity structure with pixel-velocity two-point correlation functions. Absorbers with the largest velocity dispersions are associated with blue, face-on ($i<57^{\circ}$) galaxies probed along the projected minor axis ($\Phi \geq 45^{\circ}$), while those with the smallest velocity dispersions belong to red, face-on galaxies along the minor axis. The velocity structure is similar for edge-on ($i \geq 57^{\circ}$) galaxies regardless of galaxy color or azimuthal angle, for red galaxies with azimuthal angle, and for blue and red galaxies probed along the projected major axis ($\Phi<45^{\circ}$). The cloud column densities for face-on galaxies and red galaxies are smaller than for edge-on galaxies and blue galaxies, respectively. These results are consistent with biconical outflows along the minor axis for star-forming galaxies and accreting and/or rotating gas, which is most easily observed in edge-on galaxies probed along the major axis. Gas entrained in outflows may be fragmented with large velocity dispersions, while gas accreting onto or rotating around galaxies may be more coherent due to large path lengths and smaller velocity dispersions. Quiescent galaxies may exhibit little-to-no outflows along the minor axis, while accretion/rotation may exist along the major axis.Comment: 12 pages, 6 figures, 1 table. Accepted for publication in Ap