X. F. Liu

Indirect control of quantum systems via an accessor: pure coherent control without system excitation

A pure indirect control of quantum systems via a quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite-dimensional quantum systems and exemplified by two- and three-dimensional systems. The scheme exhibits some advantages; it uses less qubits in the accessor and does not depend on the energy-level structure of the controlled system.

Quantum thermalization with couplings

We present an exactly solvable model to study the role of the system-bath coupling for the generalized canonical thermalization, which reduces almost all the pure states of the universe (formed by a system S plus its surrounding heat bath B) to a canonical equilibrium state of S. It is found that, for the overwhelming majority of the universe states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, a decoherence mechanism is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. The nonvanishing off-diagonal elements due to the finite size of the bath and the stronger system-bath interaction might offer more to quantum thermalization.

Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling

D. Z. Xu, Sheng-Wen Li, X. F. Liu, and C. P. Sun State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190, China Beijing Computational Science Research Center, Beijing 100084, China Department of Mathematics, Peking University, Beijing 100871, China Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

Objectivity in Quantum Measurement

The objectivity is a basic requirement for the measurements in the classical world, namely, different observers must reach a consensus on their measurement results, so that they believe that the object exists “objectively” since whoever measures it obtains the same result. We find that this simple requirement of objectivity indeed imposes an important constraint upon quantum measurements, i.e., if two or more observers could reach a consensus on their quantum measurement results, their measurement basis must be orthogonal vector sets. This naturally explains why quantum measurements are based on orthogonal vector basis, which is proposed as one of the axioms in textbooks of quantum mechanics. The role of the macroscopicality of the observers in an objective measurement is discussed, which supports the belief that macroscopicality is a characteristic of classicality.

Quantum state reconstruction of many body system based on complete set of quantum correlations

We propose and study a universal approach for the reconstruction of quantum states of many body systems from symmetry analysis. The concept of minimal complete set of quantum correlation functions (MCSQCF) is introduced to describe the state reconstruction. As an experimentally feasible physical object, the MCSQCF is mathematically defined through the minimal complete subspace of observables determined by the symmetry of quantum states under consideration. An example with broken symmetry is analyzed in detail to illustrate the idea.

Boson realizations of quantum algebras and some physical spaces with quantum algebra symmetry

The generators ofq-boson algebra are expressed in terms of those of boson algebra, and the relations among the representations of a quantum algebra onq-Fock space, on Fock space, and on coherent state space are discussed in a general way. Two examples are also given to present concrete physical spaces with quantum algebra symmetry. Finally, a new homomorphic mapping from a Lie algebra to boson algebra is presented.