Tsubasa Ichikawa

Duality, phase structures, and dilemmas in symmetric quantum games

Abstract Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners’ Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD, and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided.

Concatenated Composite Pulses Compensating Simultaneous Systematic Errors

In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.

Exchange Symmetry and Multipartite Entanglement

Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group

Geometric aspects of composite pulses.

{S}_{N}

Designing robust unitary gates: Application to concatenated composite pulses

. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that antisymmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group

Testing EPR locality using B-mesons

{B}_{N}

Minimal and robust composite two-qubit gates with Ising-type interaction

must also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.

Entanglement measures for intermediate separability of quantum states

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses—one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system—have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.

Equation of state for the one-dimensional attractive δ -potential Bose gas in the weak-coupling regime

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.

QUANTUM ORACLES IN TERMS OF UNIVERSAL GATE SET

We study the possibility of testing local realistic theory (LRT) based on the Bell inequality for the correlations in the decay modes of entangled K or B-mesons. It is shown that such a test is possible for a restricted class of LRT, despite the passive nature of decay events and/or the non-unitary treatment of the correlations which invalidate the test for general LRT. Unfortunately, the present setup of the KEKB (Belle) experiment, where the coherence of entangled B-mesons has been confirmed recently, does not admit such a test due to the indeterminacy in the separate decay times of the entangled pairs.