arXiv subjects
Publications and source records attributed to C. H. Oh.
A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.
We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.
We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space. For a given path, there are infinite Hamiltonians which can realize the same evolution. A general form of the Hamiltonians is constructed in which one may select the desired one for implementing a prescribed evolution. This scheme can be generalized to higher dimensional systems.
When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloning, using nuclear magnetic resonance techniques. Our experiments may further have important implications into many quantum information processing protocols.
We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system - a frequency- and spatially degenerate two-photon field. The method of statistical estimation of the quantum state based on solving the likelihood equation and analyzing the statistical properties of the obtained estimates is developed. Using the root approach of estimating quantum states, the initial two-photon state vector is reproduced from the measured fourth moments in the field . The developed approach applied to quantum states reconstruction is based on the amplitudes of mutually complementary processes. Classical algorithm of statistical estimation based on the Fisher information matrix is generalized to the case of quantum systems obeying Bohr's complementarity principle. It has been experimentally proved that biphoton-qutrit states can be reconstructed with the fidelity of 0.995-0.999 and higher.
We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.
We describe a nuclear magnetic resonance (NMR) experiment which implements an efficient one-to-two qubit phase-covariant cloning machine(QPCCM). In the experiment we have achieved remarkably high fidelities of cloning, 0.848 and 0.844 respectively for the original and the blank qubit. This experimental value is close to the optimal theoretical value of 0.854. We have also demonstrated how to use our phase-covariant cloning machine for quantum simulations of bit by bit eavesdropping in the four-state quantum key distribution protocol.
This paper focuses on the geometric phase of entangled states of bi-partite systems under bi-local unitary evolution. We investigate the relation between the geometric phase of the system and those of the subsystems. It is shown that (1) the geometric phase of cyclic entangled states with non-degenerate eigenvalues can always be decomposed into a sum of weighted non-modular pure state phases pertaining to the separable components of the Schmidt decomposition, though the same cannot be said in the non-cyclic case, and (2) the geometric phase of the mixed state of one subsystem is generally different from that of the entangled state even by keeping the other subsystem fixed, but the two phases are the same when the evolution operator satisfies conditions where each component in the Schmidt decomposition is parallel transported.
We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the outcome of the tomography is consistent with unbiased noise in the channel. We study the incoherent eavesdropping attacks that are still permissible and establish under which conditions a secure cryptographic key can be generated. The whole analysis is carried out for channels that transmit quantum systems of any finite dimension.
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.
It was shown in Phys. Rev. Lett., 87, 230402 (2001) that N (N >= 4) qubits described by a certain one parameter family F of bound entangled states violate Mermin-Klyshko inequality for N >= 8. In this paper we prove that the states from the family F violate Bell inequalities derived in Phys. Rev. A, 56, R1682 (1997), in which each observer measures three non-commuting sets of orthogonal projectors, for N >=7. We also derive a simple one parameter family of entanglement witnesses that detect entanglement for all the states belonging to F. It is possible that these new entanglement witnesses could be generated by some Bell inequalities.
In this paper we show a Bell inequality of Clauser-Horne type for three three-dimensional systems (qutrits). Violation of the inequality by quantum mechanics is shown for the case in which each of the three observers measures two non-commuting observables, defined by the so called unbiased symmetric six port beamsplitters, on a maximally entangled state of three qutrits. The strength of the violation of the inequality agrees with the numerical results presented in Kaszlikowski et. al., quant-ph//0202019.
We present numerical data showing, that three qutrit correlations for a pure state, which is not maximally entangled, violate local realism more strongly than three-qubit correlations. The strength of violation is measured by the minimal amount of noise that must be admixed to the system so that the noisy correlations have a local and realistic model.
In this brief report we show the new Bell-Clauser-Horne inequality for two entangled three dimensional quantum systems (so called qutrits). This inequality is violated by a maximally entangled state of two qutrits observed via symmetric three input and three output port beamsplitter only if the amount of noise in the system equals ${11-6\sqrt3 \over 2}\approx 0.308$. This is in perfect agreement with the previous numerical calculations presented in Kaszlikowski {\it et. al.} Phys. Rev. Lett. {\bf 85}, 4418 (2000).
In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled $N$-dimensional ($3 \leq N$) quantum objects is stronger than for two maximally entangled qubits and grows with $N$. In this paper we present the analytical proof of this fact for N=3.
We report on the effects of a simple decoherence model on the quantum search algorithm. Despite its simplicity, the decoherence model is an instructive model that can genuinely imitate realistic noisy environment in many situations. As one would expect, as the size of the database gets larger, the effects of decoherence on the efficiency of the quantum search algorithm cannot be ignored. Moreover, with decoherence, it may not be useful to iterate beyond the first maxima in the probability distribution of the search entry. Surprisingly, we also find that the number of iterations for maximum probability of the search entry reduces with decoherence.
We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.