Tohya Hiroshima

Quantum information with Gaussian states

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states.

Maximally entangled mixed states under nonlocal unitary operations in two qubits

We propose novel mixed states in two qubits, “maximally entangled mixed states”, which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven when the rank of the states is less than 4, and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with same eigenvalues.

Quantum-confined Stark effect in graded-gap quantum wells

Exciton states in AlxGa1−xAs graded‐gap quantum well structures with an electric field perpendicular to the layer have been calculated. The calculations show that, for the ground‐state heavy‐hole exciton in this quantum well structure, the dependence of Stark shift and the oscillator strengths on the external electric field is quite different from the case of the usual square‐shaped quantum well structure, whereas for the ground‐state light‐hole exciton there is no significant difference between these two quantum well structures. These results can be interpreted in terms of the difference between the heavy‐hole effective mass and the light‐hole one.

Enhancement of quantum confined Stark effect in a graded gap quantum well

A graded gap quantum well structure, where the band gap is linearly changing along the growth direction, is proposed for the enhancement of quantum confined Stark effect. Theoretical calculations show that the ground‐state exciton peak energy shifts by a larger amount than in a usual square‐shaped quantum well under an applied electric field. The wave function modifications in this quantum well result in a smaller decrease of the exciton oscillator strength, according to the electric field applied. These effects reveal the possibility of achieving high‐performance optical modulators or other devices which utilize the quantum confined Stark effect.

Optimal dense coding with mixed state entanglement

I investigate dense coding with a general mixed state on the Hilbert space Cd ⊗ Cd shared between a sender and receiver. The following result is proved. When the sender prepares the signal states by mutually orthogonal unitary transformations with equal a priori probabilities, the capacity of dense coding is maximized. It is also proved that the optimal capacity of dense coding χ* satisfies ER(ρ) ≤ χ* ≤ ER(ρ) + log2 d, where ER(ρ) is the relative entropy of entanglement of the shared entangled state.

Quantum teleportation scheme by selecting one of multiple output ports

The scheme of quantum teleportation, where Bob has multiple

Effect of conduction‐band nonparabolicity on quantized energy levels of a quantum well

(N)

Electric field induced refractive index changes in GaAs‐AlxGa1−xAs quantum wells

output ports and obtains the teleported state by simply selecting one of the

Monogamy inequality for distributed gaussian entanglement.

N

Majorization criterion for distillability of a bipartite quantum state

ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alices measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of