Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations

A remarkable feature of typical ground states of strongly-correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant upper-bound on the entanglement entropy, called the area law. However, the known bound exists only in a hypothetical limit, rendering its physical relevance highly questionable. In this paper, we give a simple proof of the area law for entanglement entropy in one dimension under the condition of exponentially decaying correlations. Our proof dramatically reduces the previously known bound on the entanglement entropy, bringing it, for the first time, into a realistic regime. The proof is composed of several simple and straightforward steps based on elementary quantum information tools. We discuss the underlying physical picture, based on a renormalization-like construction underpinning the proof, which transforms the entanglement entropy of a continuous region into a sum of mutual informations in different length scales and the entanglement entropy at the boundary

Addressing individual atoms in optical lattices with standing-wave driving fields

A scheme for addressing individual atoms in one- or two-dimensional optical lattices loaded with one atom per site is proposed. The scheme is based on position-dependent atomic population transfer induced by several standing-wave driving fields. This allows various operations important in quantum information processing, such as manipulation and measurement of any single atom, two-qubit operations between any pair of adjacent atoms, and patterned loading of the lattice with one atom per every nth site for arbitrary n. The proposed scheme is robust against considerable imperfections and actually within reach of current technology.Comment: 4 pages, 3 figures; minor revision

Quantum Teleportation with Atoms Trapped in Cavities

We propose a scheme to implement the quantum teleportation protocol with single atoms trapped in cavities. The scheme is based on the adiabatic passage and the polarization measurement. We show that it is possible to teleport the internal state of an atom trapped in a cavity to an atom trapped in another cavity with the success probability of 1/2 and the fidelity of 1. The scheme is resistant to a number of considerable imperfections such as the violation of the Lamb-Dicke condition, weak atom-cavity coupling, spontaneous emission, and detection inefficiency

Quantum Computation by Cooling

Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an intricate many-body Hamiltonian makes its analysis daunting. While it is plausible to directly cool the final gapped system of the adiabatic evolution instead, the analysis of such a scheme on a general ground is missing. Here, we propose a specific Hamiltonian model for this purpose. The scheme is inspired by cavity cooling, involving the emulation of a zero-temperature reservoir. Repeated discarding of ancilla reservoir qubits extracts the entropy of the system, driving the system toward its ground state. At the same time, the measurement of the discarded qubits hints at the energy level structure of the system as a return. We show that quantum computation based on this cooling procedure is equivalent in its computational power to the one based on quantum circuits. We then exemplify the scheme with a few illustrative use cases for combinatorial optimization problems. In the first example, the cooling is free from any local energy minima, reducing the scheme to Grover's search algorithm with a few improvements. In the second example, the cooling suffers from abundant local energy minima. To circumvent this, we implant a mechanism in the Hamiltonian so that the population trapped in the local minima can tunnel out by high-order transitions. We support this idea with a numerical simulation for a particular combinatorial optimization problem. We also discuss its application to preparing quantum many-body ground states, arguing that the spectral gap is a crucial factor in determining the time scale of the cooling.Comment: 8 pages, 3 figure

Two-dimensional imaging of gauge fields in optical lattices

We propose a scheme to generate an arbitrary Abelian vector potential for atoms trapped in a two-dimensional optical lattice. By making the optical lattice potential dependent on the atomic state, we transform the problem into that of a two-dimensional imaging. It is shown that an arbitrarily fine pattern of the gauge field in the lattice can be realized without need of diffraction-limited imaging.Comment: 4 pages, 3 figure

Generation of Atomic Cluster States through the Cavity Input-Output Process

We propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. Our scheme is based on the cavity input-output process and the single photon polarization measurement. We show that, even with the practical imperfections such as atomic spontaneous emission, weak atom-cavity coupling, violation of the Lamb-Dicke condition, cavity photon loss, and detection inefficiency, the proposed gate is feasible for generation of a cluster state in that it meets the scalability criterion and it operates in a conclusive manner. We demonstrate a simple and efficient process to generate a cluster state with our high probabilistic entangling gate