arXiv subjects

Yutaka Shikano

Publications and source records attributed to Yutaka Shikano.

At least 55 records · Page 3Linked to original sources

arXiv2014

Discrete-time quantum walk with feed-forward quantum coin

Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport.

quant-ph↗

arXiv2013

Discrete time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit

We propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasi-magnon field realized in an ensemble of nitrogen-vacancy centres in diamond. The coin is realized as a superconducting flux qubit. Our scheme improves on an existing proposal for implementing quantum walks in cavity quantum electrodynamics by removing the cumbersome requirement of varying drive-pulse durations according to mean quasiparticle number. Our improvement is relevant to all indirect-coin-flip cavity quantum-electrodynamics realizations of quantum walks. Our numerical analysis shows that this scheme can realize a discrete quantum walk under realistic conditions.

quant-ph↗

arXiv2013

From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution

The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic behavior, of the one-dimensional discrete time quantum walk is analytically shown. From the limit distribution of the discrete time quantum walk, the discrete time quantum walk can be taken as the quantum dynamical simulator of some physical systems.

quant-ph↗

arXiv2013

Temperature Dependence of Highly Excited Exciton Polaritons in Semiconductor Microcavities

Observations of polariton condensation in semiconductor microcavities suggest that polaritons can be exploited as a novel type of laser with low input-power requirements. The low-excitation regime is approximately equivalent to thermal equilibrium, and a higher excitation results in more dominant nonequilibrium features. Although standard photon lasing has been experimentally observed in the high excitation regime, e-h pair binding can still remain even in the high-excitation regime theoretically. Therefore, the photoluminescence with a different photon lasing mechanism is predicted to be different from that with a standard photon lasing. In this paper, we report the temperature dependence of the change in photoluminescence with the excitation density. The second threshold behavior transited to the standard photon lasing is not measured at a low-temperature, high-excitation power regime. Our results suggest that there may still be an electron--hole pair at this regime to give a different photon lasing mechanism.

cond-mat.mes-hall↗

arXiv2013

Reply to "Comment on `Optimal probe wave function of weak-value amplification' "

It is pointed out that the "counter example" presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense that we have to gauge fix the freedom of the phase translation. It is shown that there are two kinds of solutions, normalizable and un-normalizable. The former is our optimal solution, and the latter is what he found. It seems only the former is relevant from a practical point of view.

quant-ph↗

arXiv2012

Extracting joint weak values from two-dimensional spatial displacements

The joint weak value is a counterfactual quantity related to quantum correlations and quantum dynamics, which can be retrieved via weak measurements, as initiated by Aharonov and colleagues. In this Rapid Communication, we provide a full analytical extension of the method described by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint weak values of single-particle operators from two-dimensional spatial displacements of Laguerre-Gauss probe states, for the case of azimuthal index |l|>1. This method has a statistical advantage over previous ones since information about the conjugate observable, i.e., the momentum displacement of the probe, is not required. Moreover, we demonstrate that under certain conditions, the joint weak value can be extracted directly from spatial displacements without any additional data processing.

quant-ph↗

arXiv2012

Optimal Probe Wavefunction of Weak-Value Amplification

The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.

quant-ph↗

arXiv2012

Theory of "Weak Value" and Quantum Mechanical Measurements

We review the definition and the concepts of the weak values and some measurement model to extract the weak value. This material is based on the author Ph.D. thesis "Time in Weak Values and Discrete Time Quantum Walk" at Tokyo Institute of Technology (2011).

quant-ph↗

arXiv2011

Notes on Inhomogeneous Quantum Walks

We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which resembles the Hofstadter butterfly.

quant-ph↗

arXiv2011

Maxwell's Demon and Data Compression

In an asymmetric Szilard engine model of Maxwell's demon, we show the equivalence between information theoretical and thermodynamic entropies when the demon erases information optimally. The work gain by the engine can be exactly canceled out by the work necessary to reset demon's memory after optimal data compression a la Shannon before the erasure.

physics.class-ph↗

arXiv2011

Estimation of Spin-Spin Interaction by Weak Measurement Scheme

Precisely knowing an interaction Hamiltonian is crucial to realize quantum information tasks, especially to experimentally demonstrate a quantum computer and a quantum memory. We propose a scheme to experimentally evaluate the spin-spin interaction for a two-qubit system by the weak measurement technique initiated by Yakir Aharonov and his colleagues. Furthermore, we numerically confirm our proposed scheme in a specific system of a nitrogen vacancy center in diamond. This means that the weak measurement can also be taken as a concrete example of the quantum process tomography.

quant-ph↗

arXiv2011

A reply to "Problems with modelling closed timelike curves as post-selected teleportation"

In arXiv:1107.4675 Ralph uses our post-selection model of closed timelike curves (P-CTC) to construct an "unproven-theorem" paradox, and claims that this voids our argument that P-CTCs are able to resolve such types of paradoxes. Here we point out that Ralph has not accounted for all the interactions needed for his construction. A more careful analysis confirms that indeed there is no paradox, contrary to his claims.

quant-ph↗

arXiv2011

Crossovers induced by discrete-time quantum walks

We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in some limit. At first we generalize our previous study [Phys. Rev. A \textbf{81}, 062129 (2010)] on the DTQW with position measurements. We show that the position measurements per each step with probability $p \sim 1/n^β$ can be evaluated, where $n$ is the final time and $0<β<1$. We also give a corresponding continuous-time case. As a consequence, crossovers from the diffusive spreading (random walk) to the ballistic spreading (quantum walk) can be seen as the parameter $β$ shifts from 0 to 1 in both discrete- and continuous-time cases of the weak convergence theorems. Secondly, we introduce a new class of the DTQW, in which the absolute value of the diagonal parts of the quantum coin is proportional to a power of the inverse of the final time $n$. This is called a final-time-dependent DTQW (FTD-DTQW). The CTQW is obtained in a limit of the FTD-DTQW. We also obtain the weak convergence theorem for the FTD-DTQW which shows a variety of spreading properties. Finally, we consider the FTD-DTQW with periodic position measurements. This weak convergence theorem gives a phase diagram which maps sufficiently long-time behaviors of the discrete- and continuous-time quantum and random walks.

quant-ph↗

arXiv2011

Survival probability in a one-dimensional quantum walk on a trapped lattice

The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical walkers. It is shown that the time dependence of survival probability of quantum walkers has a piecewise stretched exponential character depending on the density of traps in numerical and analytical observations. The crossover between the quantum analogs of the Rosenstock and Donsker-Varadhan behaviors is identified.

quant-ph↗

arXiv2010

Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasi-periodic potential. When the period of coin operators is incommensurate to the lattice spacing, we rigorously show that the limit distribution of the quantum walk is localized at the origin. We also numerically study the eigenvalues of the one-step time evolution operator and find the Hofstadter butterfly spectrum which indicates the fractal nature of this class of quantum walks.

quant-ph↗

arXiv2010

Strange Weak Values

We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a negative weak value of a given projection operator and strange values of an observable in general. The general framework is applied to Hardy's paradox and the spin $1/2$ system to explicitly address the issues of counter-factuality and strange weak values. The counter-factual arguments which characterize the paradox specifies the pre-selected state and a complete set of the post-selected states clarifies how the strange weak values emerge.

quant-ph↗

arXiv2010

Role of a Phase Factor in the Boundary Condition of a One-Dimensional Junction

One-dimensional quantum systems can be experimentally studied in recent nano-technology like the carbon nanotube and the nanowire. We have considered the mathematical model of the one-dimensional Schrödinger particle with a junction and have analyzed the phase factor in the boundary condition of the junction. We have shown that the phase factor in the tunneling case appears in the situation of the non-adiabatic transition with the three energy levels in the exact WKB analysis.

quant-ph↗

arXiv2010

The quantum mechanics of time travel through post-selected teleportation

This paper discusses the quantum mechanics of closed timelike curves (CTC) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is physically inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum field theory in curved spacetime). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general relativistic closed timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

quant-ph↗