49,847 research outputs found

    Fast Polarization for Processes with Memory

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    Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. Namely, previous works have not addressed fast polarization of the high entropy set under memory. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite-state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both for the high and for the low entropy sets.Comment: 17 pages, 3 figures. Submitted to IEEE Transactions on Information Theor

    Finite temperature effects on spin polarization of neutron matter in a strong magnetic field

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    Spin polarization of neutron matter at finite temperatures and strong magnetic fields up to 101810^{18} G is studied in the model with the Skyrme effective interaction. It is shown that, together with the thermodynamically stable branch of solutions for the spin polarization parameter corresponding to the case when the majority of neutron spins are oriented opposite to the direction of the magnetic field (negative spin polarization), the self-consistent equations, beginning from some threshold density, have also two other branches of solutions corresponding to positive spin polarization. The influence of finite temperatures on spin polarization remains moderate in the Skyrme model up to temperatures relevant for protoneutron stars, and, in particular, the scenario with the metastable state characterized by positive spin polarization, considered at zero temperature in Phys. Rev. C {\bf 80}, 065801 (2009), is preserved at finite temperatures as well. It is shown that above certain density the entropy for various branches of spin polarization in neutron matter with the Skyrme interaction in a strong magnetic field demonstrates the unusual behavior being larger than that of the nonpolarized state. By providing the corresponding low-temperature analysis, it is clarified that this unexpected behavior should be addressed to the dependence of the entropy of a spin polarized state on the effective masses of neutrons with spin up and spin down, and to a certain constraint on them which is violated in the respective density range.Comment: Prepared with RevTeX4, 6pp., 4 figs; v2: accepted in JKA

    Demonstration of an optical-coherence converter

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    Studying the coherence of an optical field is typically compartmentalized with respect to its different optical degrees of freedom (DoFs) -- spatial, temporal, and polarization. Although this traditional approach succeeds when the DoFs are uncoupled, it fails at capturing key features of the field's coherence if the DOFs are indeed correlated -- a situation that arises often. By viewing coherence as a `resource' that can be shared among the DoFs, it becomes possible to convert the entropy associated with the fluctuations in one DoF to another DoF that is initially fluctuation-free. Here, we verify experimentally that coherence can indeed be reversibly exchanged -- without loss of energy -- between polarization and the spatial DoF of a partially coherent field. Starting from a linearly polarized spatially incoherent field -- one that produces no spatial interference fringes -- we obtain a spatially coherent field that is unpolarized. By reallocating the entropy to polarization, the field becomes invariant with regards to the action of a polarization scrambler, thus suggesting a strategy for avoiding the deleterious effects of a randomizing system on a DoF of the optical field.Comment: 7 pages; 6 figure

    Determination of optimal reversed field with maximal electrocaloric cooling by a direct entropy analysis

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    Application of a negative field on a positively poled ferroelectric sample can enhance the electrocaloric cooling and appears as a promising method to optimize the electrocaloric cycle. Experimental measurements show that the maximal cooling does not appear at the zero-polarization point, but around the shoulder of the P-E loop. This phenomenon cannot be explained by the theory based on the constant total entropy assumption under adiabatic condition. In fact, adiabatic condition does not imply constant total entropy when irreversibility is involved. A direct entropy analysis approach based on work loss is proposed in this work, which takes the entropy contribution of the irreversible process into account. The optimal reversed field determined by this approach agrees with the experimental observations. This study signifies the importance of considering the irreversible process in the electrocaloric cycles

    Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

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    The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger Finite-Size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit

    Secure self-calibrating quantum random bit generator

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    Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the "min-entropy" of the system, and we employ this value to distill a truly random bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.Comment: 5 pages, 2 figure

    Quantum entanglement in strong-field ionization

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    We investigate the time-evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion-core. Since the standard procedure is numerically prohibitive in this case, we propose a novel way to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime
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