A fundamental task in quantum information science is to transfer an unknown state from particle $A$ to particle $B$ (often in remote space locations) by using a bipartite quantum operation $mathcal{E}^{AB}$. We suggest the power of $mathcal{E}^{AB}$
for quantum state transfer (QST) to be the maximal average probability of QST over the initial states of particle $B$ and the identifications of the state vectors between $A$ and $B$. We find the QST power of a bipartite quantum operations satisfies four desired properties between two $d$-dimensional Hilbert spaces. When $A$ and $B$ are qubits, the analytical expressions of the QST power is given. In particular, we obtain the exact results of the QST power for a general two-qubit unitary transformation.
Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interest
ed in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles.
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that these two to
ols may give different conclusions about the order of the degrees of correlation in two specific two-qubit states. This result implies that the orderings of bipartite quantum states according to the degrees of correlation depend on which correlation measure we adopt.
We develop a numerical algorithm to calculate the degrees of irreducible multiparty correlations for an arbitrary multiparty quantum state, which is efficient for any quantum state of up to five qubits. We demonstrate the power of the algorithm by th
e explicit calculations of the degrees of irreducible multiparty correlations in the 4-qubit GHZ state, the Smolin state, and the 5-qubit W state. This development takes a crucial step towards practical applications of irreducible multiparty correlations in real quantum many-body physics.
Generalizing Amaris work titled Information geometry on hierarchy of probability distributions, we define the degrees of irreducible multiparty correlations in a multiparty quantum state based on quantum relative entropy. We prove that these definiti
ons are equivalent to those derived from the maximal von Neaumann entropy principle. Based on these definitions, we find a counterintuitive result on irreducible multiparty correlations: although the degree of the total correlation in a three-party quantum state does not increase under local operations, the irreducible three-party correlation can be created by local operations from a three-party state with only irreducible two-party correlations. In other words, even if a three-party state is initially completely determined by measuring two-party Hermitian operators, the determination of the state after local operations have to resort to the measurements of three-party Hermitian operators.
The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations existing for the state. W
e find that the stabilizer dimension of an $n$-qubit ($nge 2$) graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit ($nge 3$) graph state is equal to the degree of irreducible two-qubit correlations in the state.
We identify the correlation in a state of two identical particles as the residual information beyond what is already contained in the 1-particle reduced density matrix, and propose a correlation measure based on the maximum entropy principle. We obta
in the analytical results of the correlation measure, which make it computable for arbitrary two-particle states. We also show that the degrees of correlation in the same two-particle states with different particle types will decrease in the following order: bosons, fermions, and distinguishable particles.
In a system of $n$ quantum particles, the correlations are classified into a series of irreducible $k$-particle correlations ($2le kle n$), where the irreducible $k$-particle correlation is the correlation appearing in the states of $k$ particles but
not existing in the states of $k-1$ particles. A measure of the degree of irreducible $k$-particle correlation is defined based on the maximal entropy construction. By adopting a continuity approach, we overcome the difficulties in calculating the degrees of irreducible multi-particle correlations for the multi-particle states without maximal rank. In particular, we obtain the degrees of irreducible multi-particle correlations in the $n$-qubit stabilizer states and the $n$-qubit generalized GHZ states, which reveals the distribution of multi-particle correlations in these states.
We present a semi-classical theory for light deflection by a coherent $Lambda$-type three-level atomic medium in an inhomogeneous magnetic field or an inhomogeneous control laser. When the atomic energy levels (or the Rabi coupling by the control las
er) are position-dependent due to the Zeeman effect by the inhomogeneous magnetic field (or the inhomogeneity of the control field profile), the spatial dependence of the refraction index of the atomic medium will result in an observable deflection of slow signal light when the electromagnetically induced transparency happens to avoid medium absorption. Our theoretical approach based on Fermats principle in geometrical optics not only provides a consistent explanation for the most recent experiment in a straightforward way, but also predicts the new effects for the slow signal light deflection by the atomic media in an inhomogeneous off-resonant control laser field.
