From pure quantum states to quantum classical systems

Two types of Hamiltonian hybrid quantum-classical theories are considered as potential models of the quantum measurement process. The two theories have the same Hamiltonian dynamics but differ in the association of states of the quantum system with states of the hybrid model. In the first type of association pure quantum states are modeled by pure states of the hybrid, while in the second type the pure quantum states are modeled by statistical mixtures of the hybrid pure states. It is shown that the second of the two theories describes correctly the quantum measurement while the first provides only an averaged description.Two types of Hamiltonian hybrid quantum-classical theories are considered as potential models of the quantum measurement process. The two theories have the same Hamiltonian dynamics but differ in the association of states of the quantum system with states of the hybrid model. In the first type of association pure quantum states are modeled by pure states of the hybrid, while in the second type the pure quantum states are modeled by statistical mixtures of the hybrid pure states. It is shown that the second of the two theories describes correctly the quantum measurement while the first provides only an averaged description.

Physical Review AMay 31, 20138 citations

Optimizing classical communication in remote preparation of a general pure qubit

Congyi Hua, Yixin Chen

How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.

arXiv:1405.5309May 21, 20140 citations

Classical Systems in Quantum Mechanics

Pavel Bóna

arXiv:1911.02081Springer eBooksJan 1, 20203 citations

Stability of Quantum States of Finite Macroscopic Systems against Classical Noises, Perturbations from Environments, and Local Measurements

Akira Shimizu, Takayuki Miyadera

We study the stability of quantum states of macroscopic systems of finite volume V. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.We study the stability of quantum states of macroscopic systems of finite volume V. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.

arXiv:quant-ph/0203106Physical Review LettersDec 16, 200293 citations

Continuous transition from quantum to classical system

T. Yoneda, Aya Nagasato, Tatsuo Akamine +1 more

Il Nuovo Cimento BMay 1, 20010 citations

N

points on the Bloch sphere, which provides a geometric description.