An Information--Theoretic Equality Implying the Jarzynski Relation

We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement outcomes of the earlier and later projective measurements. We show that it also contains the Jarzynski relation between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. Our result elucidates the information-theoretic underpinning of thermodynamics and explains why the Jarzynski relation holds identically both quantumly as well as classically.Comment: 2 pages, no figure

Hide and seek on complex networks

Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social-, man-made and biological networks. We find that human networks of governance and collaboration are predictable on teat-a-teat level, reflecting well defined pathways, but globally inefficient. In contrast, the Internet tends to have better overall communication abilities, more alternative pathways, and is therefore more robust. Between these extremes the molecular network of Saccharomyces cerevisea is more similar to the simpler social systems, whereas the pattern of interactions in the more complex Drosophilia melanogaster, resembles the robust Internet.Comment: 5 pages, 5 figure

Classical Correlations and Entanglement in Quantum Measurements

We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is instead equal to the degree of classical correlations between the two. As a consequence, we derive an uncertainty-like expression relating the information gain in the measurement and the initial mixedness of the apparatus. Final entanglement between the environment and the apparatus is also shown to be relevant for the efficiency of the measurement.Comment: to appear in Physical Review Letter

Improving Detectors Using Entangling Quantum Copiers

We present a detection scheme which using imperfect detectors, and imperfect quantum copying machines (which entangle the copies), allows one to extract more information from an incoming signal, than with the imperfect detectors alone.Comment: 4 pages, 2 figures, REVTeX, to be published in Phys. Rev.

Simple observations concerning black holes and probability

It is argued that black holes and the limit distributions of probability theory share several properties when their entropy and information content are compared. In particular the no-hair theorem, the entropy maximization and holographic bound, and the quantization of entropy of black holes have their respective analogues for stable limit distributions. This observation suggests that the central limit theorem can play a fundamental role in black hole statistical mechanics and in a possibly emergent nature of gravity.Comment: 6 pages Latex, final version. Essay awarded "Honorable Mention" in the Gravity Research Foundation 2009 Essay Competitio

Phase diagram of the spin-1/2 J1J_1-J2J_2-J3J_3 Heisenberg model on the square lattice

We presents the results of an extensive numerical study of the phase diagram of the spin-1/2, \protect{$J_1$-$J_2$-$J_3$} Heisenberg model on a square lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor interactions $J_1$, using exact diagonalization with periodic and twisted boundary conditions. Comparison is made with published spin wave calculations. We show that quantum fluctuations play a very important role, changing both the extent and the wave vector of classical spiral phases, and leading to new quantum phases where the classical spiral states have a high degeneracy. These include a new phase with small or vanishing spin-stiffness, in addition to known valence-bond-solid and bond-nematic phases.Comment: submitted for the International Conference on Magnetism to be held 26-31 July 2009 in Karlsruh

Incomplete quantum process tomography and principle of maximal entropy

The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state associated with the quantum process via Choi-Jamiolkowski isomorphism. It will be shown that an arbitrary process estimation experiment can be reformulated in a unified framework and MaxEnt principle can be consistently exploited. We will argue that the suggested choice for the process entropy satisfies natural list of properties and it reduces to the state MaxEnt principle, if applied to preparator devices.Comment: 8 pages, comments welcome, references adde

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl