scholarly journals Kelly Betting with Quantum Payoff: a continuous variable approach

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 545
Author(s):  
Salvatore Tirone ◽  
Maddalena Ghio ◽  
Giulia Livieri ◽  
Vittorio Giovannetti ◽  
Stefano Marmi
Keyword(s):  
Degrees Of Freedom ◽  
Classical Model ◽  
Single Mode ◽  
Continuous Variable ◽  
Quantum Memory ◽  
Memory Element ◽  
Gaussian Channels ◽  
Variable Approach ◽  
Gaussian Density ◽  
Quantum Analog

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude.

scholarly journals Entanglement in massive coupled oscillators

2011 ◽  
Vol 11 (3&4) ◽  
pp. 278-299
Author(s):  
Nathan L. Harshman ◽  
William F. Flynn
Keyword(s):  
Coupled Oscillators ◽  
Coherent States ◽  
Degrees Of Freedom ◽  
Classical Model ◽  
Reduced Density Matrix ◽  
One Dimension ◽  
Atomic Position ◽  
Pure States ◽  
Non Gaussian ◽  
Reduced Density

This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive particles with two degrees of freedom and a quadratic Hamiltonian. We present two methods, one analytic and one approximate, to calculate the interatomic entanglement for Gaussian and non-Gaussian pure states as measured by the purity of the reduced density matrix. The cases of free and trapped molecules and hetero- and homonuclear molecules are treated. In general, when the trap frequency and the molecular frequency are very different, and when the atomic masses are equal, the atoms are highly-entangled for molecular coherent states and number states. Surprisingly, while the interatomic entanglement can be quite large even for molecular coherent states, the covariance of atomic position and momentum observables can be entirely explained by a classical model with appropriately chosen statistical uncertainty.

Cohering and decohering power of Gaussian channels

2020 ◽  
Vol 18 (04) ◽  
pp. 2050017
Author(s):  
Huazhen Yao ◽  
Jianwen Zhang ◽  
Yangyang Wang
Keyword(s):  
Relative Entropy ◽  
Thermal Noise ◽  
Continuous Variable ◽  
Basic Properties ◽  
Gaussian Channels

In this paper, we generalized the concepts of the cohering power and decohering power to Gaussian channels for continuous-variable systems with respect to coherence measures based on the relative entropy and obtained some basic properties. In addition, the cohering power and decohering power of classical noise channels, thermal noise channels and amplifier channels are calculated.

QUANTUM PHASE GATING WITH SEMICONDUCTOR QUANTUM DOTS IN A MICROCAVITY

2004 ◽  
Vol 18 (23) ◽  
pp. 1195-1203
Author(s):  
MANG FENG
Keyword(s):  
Quantum Dots ◽  
Degrees Of Freedom ◽  
Cavity Mode ◽  
Nearest Neighbor ◽  
Single Mode ◽  
Laser Pulses ◽  
Semiconductor Quantum Dots ◽  
Quantum Phase ◽  
Conduction Band Electron ◽  
Excitonic States

We propose a scheme to carry out quantum phase gate in one step by bichromatic radiation method with semiconductor quantum dots (QDs) embedded in a single mode microcavity. The spin degrees of freedom of the only excess conduction band electron are employed as qubits and excitonic states are used as auxiliary states. The nearest-neighbor coupling is not required because the cavity mode plays the role of data bus. We show how to perform quantum computing with properly tailored laser pulses and Pauli-blocking effect, without exciting the cavity mode.

scholarly journals Fidelity of Gaussian Channels

2004 ◽  
Vol 11 (04) ◽  
pp. 309-323 ◽  
Author(s):  
Carlton M. Caves ◽  
Krzysztof Wódkiewicz
Keyword(s):  
Phase Space ◽  
Scaling Law ◽  
Continuous Variable ◽  
Gaussian Channel ◽  
Quantum Cloning ◽  
Field Mode ◽  
Universal Scaling ◽  
Input Field ◽  
Gaussian Channels ◽  
Initial States

A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.

scholarly journals Multilevel Modeling of Cognitive Diagnostic Assessment: The Multilevel DINA Example

2018 ◽  
Vol 43 (1) ◽  
pp. 34-50 ◽  
Author(s):  
Wen-Chung Wang ◽  
Xue-Lan Qiu
Keyword(s):  
Continuous Variable ◽  
Parameter Recovery ◽  
Dina Model ◽  
Variable Approach ◽  
Item Level ◽  
Multivariate Bernoulli ◽  
Level Model ◽  
Log Linear ◽  
Latent Attribute ◽  
Mathematics And Science

Many multilevel linear and item response theory models have been developed to account for multilevel data structures. However, most existing cognitive diagnostic models (CDMs) are unilevel in nature and become inapplicable when data have a multilevel structure. In this study, using the log-linear CDM as the item-level model, multilevel CDMs were developed based on the latent continuous variable approach and the multivariate Bernoulli distribution approach. In a series of simulations, the newly developed multilevel deterministic input, noisy, and gate (DINA) model was used as an example to evaluate the parameter recovery and consequences of ignoring the multilevel structures. The results indicated that all parameters in the new multilevel DINA were recovered fairly well by using the freeware Just Another Gibbs Sampler (JAGS) and that ignoring multilevel structures by fitting the standard unilevel DINA model resulted in poor estimates for the student-level covariates and underestimated standard errors, as well as led to poor recovery for the latent attribute profiles for individuals. An empirical example using the 2003 Trends in International Mathematics and Science Study eighth-grade mathematical test was provided.

scholarly journals Multidimensional entanglement transport through single-mode fiber

2020 ◽  
Vol 6 (4) ◽  
pp. eaay0837 ◽  
Author(s):  
Jun Liu ◽  
Isaac Nape ◽  
Qainke Wang ◽  
Adam Vallés ◽  
Jian Wang ◽  
...  
Keyword(s):  
Hilbert Spaces ◽  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Single Mode ◽  
Single Mode Fiber ◽  
Entangled States ◽  
Spatial Mode ◽  
Alternative Approach ◽  
Spatial Modes ◽  
State Tomography

The global quantum network requires the distribution of entangled states over long distances, with substantial advances already demonstrated using polarization. While Hilbert spaces with higher dimensionality, e.g., spatial modes of light, allow higher information capacity per photon, such spatial mode entanglement transport requires custom multimode fiber and is limited by decoherence-induced mode coupling. Here, we circumvent this by transporting multidimensional entangled states down conventional single-mode fiber (SMF). By entangling the spin-orbit degrees of freedom of a biphoton pair, passing the polarization (spin) photon down the SMF while accessing multiple orbital angular momentum (orbital) subspaces with the other, we realize multidimensional entanglement transport. We show high-fidelity hybrid entanglement preservation down 250 m SMF across multiple 2 × 2 dimensions, confirmed by quantum state tomography, Bell violation measures, and a quantum eraser scheme. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fiber.

scholarly journals Mode parameterization of structures with very low symmetry: PZT and magnetite

2014 ◽  
Vol 70 (a1) ◽  
pp. C501-C501
Author(s):  
J. Manuel Perez-Mato ◽  
Balazs Kocsis ◽  
Emre Tasci ◽  
Mois Aroyo
Keyword(s):  
Degrees Of Freedom ◽  
Parent Phase ◽  
Normal Modes ◽  
Single Mode ◽  
Irreducible Representations ◽  
Mode Decomposition ◽  
Stringent Test ◽  
Low Symmetry ◽  
Distorted Phase

The parameterization of distorted structures in terms of symmetry modes is an effective and efficient method for both their description and refinement [1]. A basis of symmetry-adapted modes transforming according to irreducible representations not only provides a hierarchical division of the degrees of freedom consistent with the mechanism at the origin of the distorted phase, but it allows the avoidance of false refinement minima, typical of highly pseudo-symmetric phases. A reduction of the number of free parameters by setting to zero negligible marginal modes is also possible. The mode description is nowadays easily applicable through freely available programs [2,3], while direct single crystal and powder diffraction refinements under this parameterization are possible combining these programs with some of the most popular refinement codes. The mode description is especially effective when dealing with distorted structures of very low symmetry compared with that of the parent phase. In these cases, the hierarchy between strong primary modes and weak marginal ones is specially pronounced, minimizing the role of many secondary modes. The physical origin of each primary distortion is usually a set of unstable degenerate normal modes. This introduces correlations among the different phases in the phase diagram that become patent in a mode description and can be used both to characterize the evolution of the relevant order parameters and as a stringent test of proposed structural models. Furthermore, the fact that each of the primary mode distortions is basically associated with the activity (instability) of a single normal mode can yield a "single mode" signature in the mode decomposition, which represents a set of subtle additional structural constrains beyond conventional crystallography. We will illustrate these considerations using the examples of the monoclinic phases of ferroelectric PbZr1-xTixO3 (PZT) and the Verwey phase of magnetite.

Blip-summed quantum–classical path integral with cumulative quantum memory

2016 ◽  
Vol 195 ◽  
pp. 81-92 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Quantum Memory ◽  
Integral Methods ◽  
Acceleration Techniques ◽  
Classical Path ◽  
Forced Oscillator ◽  
Influence Functional ◽  
Harmonic Bath ◽  
Explicit Enumeration

The quantum-classical path integral (QCPI) offers a rigorous methodology for simulating quantum mechanical processes in condensed-phase environments treated in full atomistic detail. This paper describes the implementation of QCPI on system–bath models, which are frequently employed in studying the dynamics of reactive processes. The QCPI methodology incorporates all effects associated with stimulated phonon absorption and emission as its crudest limit, thus can (in some regimes) converge faster than influence functional-based path integral methods specifically designed for system–bath Hamiltonians. It is shown that the QCPI phase arising from a harmonic bath can be summed analytically with respect to the discrete bath degrees of freedom and expressed in terms of precomputed influence functional coefficients, avoiding the explicit enumeration of forced oscillator trajectories, whose number grows exponentially with the length of quantum memory. Further, adoption of the blip decomposition (which classifies the system paths based on the time length over which their forward and backward components are not identical) and a cumulative treatment of the QCPI phase between blips allows elimination of the majority of system paths, leading to a dramatic increase in efficiency. The generalization of these acceleration techniques to anharmonic environments is discussed.

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