Sachiko Kitajima

Decoherence of quantum information in the non-Markovian qubit channel

Decoherence of quantum information of qubits is investigated under the influence of the non-Markovian quantum channel, where the correlation time of reservoir variables takes a finite value. Degradation of purity, distinguishability and entanglement of qubit states are evaluated. It is found that the non-Markov effect makes the coherence time of quantum information longer than that obtained for the Markovian quantum channel. Furthermore, the quantum teleportation and quantum dense coding of qubits are considered under the influence of non-Markov channels. The fidelity between teleported and original states and the Holevo capacity are obtained.

Decoherence of entanglement in the Bloch channel

Decoherence of entanglement of qubits is investigated which is caused by the phenomenological quantum channel (the Bloch channel) equivalent to the Bloch equations. It is shown how the decoherence of entanglement depends on the longitudinal and transverse relaxation times and the equilibrium value of the qubit. The quantum dense coding system under the influence of the Bloch channel is also investigated. The Shannon mutual information obtained by the Bell measurement and the Holevo capacity is calculated. Furthermore, the microscopic system-reservoir model which yields the Bloch equations is considered. The result shows that the temperature of the thermal reservoir significantly affects the decoherence of entanglement.

Theory of decoherence control in a fluctuating environment

Detailed studies are carried out for the problem of decoherence control by a successive application of ?-pulses when a relevant spin-1/2 (qubit) system is surrounded by a stochastically fluctuating environment. Specifically, considerations are given to two representative stochastic processes: a two-state-jump Markov process and a Gauss?Markov process. Exact analytical solutions are obtained for the decoherence control by the ?-pulse application even for non-stationary stochastic processes as well as for stationary processes. In view of recent advances in dynamical decoupling experiments with artificial (engineered) stochastic noise, the results are useful in analysing qubit systems under the influence of a fluctuating environment.

Relaxation process of quantum system: Stochastic Liouville equation and initial correlation

Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.

Number-Phase Uncertainty Relation

Number-phase uncertainty relation is examined on the basis of an orthogonal phase state and a quasi-probability function. The measure of number fluctuation is not the usual standard deviation but a kind of Fisher information. This is a direct generalization to a discrete system of the corresponding quantity used recently by Hall in a theory of uncertainty for a coordinate-momentum system. It is essential to separate the “classical” part of a phase operator with the aid of the orthogonal phase state.

Dynamical processes in a generalized Coleman–Hepp model

Abstract Dynamical processes in quantum system are studied on the basis of Coleman–Hepp model. We present a theoretical framework using a spin coherent state representation. This enables us to obtain averages and quasi-probability densities which give detailed information on the dynamics of a detector as well as an incident particle. Numerical calculations are also done.

Quantum master equation approach to dynamical suppression of decoherence

An irreversible time evolution of a quantum system interacting with a surrounding environment is described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian master equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effect of the external field that is ignored in the conventional treatment. It is shown that when the external field is a sequence of phase-modulation π-pulses, the decoherence of the quantum system can be suppressed. In particular, when the pulse separation is sufficiently short in comparison with the correlation time of the environmental system, dynamical decoupling takes place. To see the effect of the phase-modulation π-pulses, the time evolution of qubit entanglement is investigated in detail.

On phase relaxation processes

Time-evolutions of two-level and multi-level systems in phase relaxation processes are investigated in a systematic way. A general form of the decoherence function which determines phase relaxation of a quantum state is obtained by making use of a microscopic interaction Hamiltonian between the relevant system and reservoir. Furthermore the loss of the phase coherence is described in terms of the Pegg–Barnett phase operator. The decoherence function is explicitly calculated for the stochastic dephasing, the boson detector model and the Coleman–Hepp model.

The classical capacity of a quantum dense coding system

Quantum dense coding transmits classical information by sending a quantum system with the assistance of quantum entanglement. The classical information capacity of a quantum dense coding system is obtained, where a sender and receiver share a completely entangled state and a quantum system encoded by applying unitary operators is sent through an arbitrary quantum channel. The result is compared with that obtained in another setting.

Quadrature operators with arbitrary phase and applications to phase-space distribution and quantum communication

Quadrature operators with arbitrary phase are studied from a point of view of the phase-space representation of quantum states, and the results are applied to simultaneous measurement and quantum communication. The Wigner function of arbitrary phase quadrature variables is introduced, which is a generalization of the usual Wigner function of position and momentum. The Kirkwood distribution is also extended for arbitrary phase quadrature variables. The simultaneous measurement of two quadrature operators is investigated using a beam splitter model and a generalized version of the Arthurs-Kelley model. The quantum teleportation of continuous variables is considered in terms of arbitrary phase quadrature variables. A general formula is derived that provides the quantum teleportation channel. The fidelity of the quantum teleportation with an uncontrollable phase is calculated for a coherent state. Furthermore, the mutual information of the quantum dense coding of continuous variables is obtained when classical information is encoded on arbitrary phase quadrature variables. The result is compared with that of the communication system, where information is transmitted using coherent and squeezed states.