Abstract:
The quantum states corresponding to a secret key are characterized using the so-called private states, where the key part consisting of a secret key is shielded by the additional systems. Based on the construction, it was shown that a secret key can be distilled from bound entangled states. In this work, I consider the shielded two-qubit states in a key-distillation scenario and derive the conditions under which a secret key can be distilled using the recurrence protocol or the two-way classical distillation, advantage distillation together with one-way postprocessing. From the security conditions, it is shown that a secret key can be distilled from bound entangled states in a much wider range. In addition, I consider the case that in which white noise is added to quantum states and show that the classical distillation protocol still works despite a certain amount of noise although the recurrence protocol does not.

Abstract:
In this letter, we show that the laser Hamiltonian can perform the quantum search. We also show that the process of quantum search is a resonance between the initial state and the target state, which implies that Nature already has a quantum search system to use a transition of energy. In addition, we provide the particular scheme to implement the quantum search algorithm based on a trapped ion.

Abstract:
In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in the algorithm. In this letter, we will supply the answer to the interesting question: can the factors seemingly harmful to a quantum algorithm(for example, perturbations) enhance the algorithm? We show that some perturbations to the generalized quantum search Hamiltonian can reduce the running time and enhance the success probability. We also provide the narrow bound to the perturbation which can be beneficial to quantum search. In addition, we show that the error induced by a perturbation on the Farhi and Gutmann Hamiltonian can be corrected by another perturbation.

Abstract:
Recently the continuous time algorithm based on the generalized quantum search Hamiltonian was presented. In this letter, we consider the running time of the generalized quantum search Hamiltonian. We provide the surprising result that the maximum speedup of quantum search in the generalized Hamiltonian is the O(1) running time regardless of the number of total states. It seems to violate the proof of Zalka that the quadratic speedup is optimal in quantum search. However the argurment of Giovannetti et al. that a quantum speedup comes from the interaction between subsystems(or, equivalently entanglement) (and is concerned with the Margolus and Levitin theorem) supports our result.

Abstract:
There are hamiltonians that solve a search problem of finding one of $N$ items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, $H_{g}$. Then the known search hamiltonians become special cases of $H_{g}$. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject only to the phase factor in $H_{g}$ and independent to the number of states or initialization.

Abstract:
We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We obtain a necessary and sufficient condition to distill a secret key using this type of schemes for Pauli qubit channels and generalized Pauli channels in higher dimension. Our results can be applied to standard protocols such as BB84 or six-state, giving a critical error rate of 20% and 27.6%, respectively. We explore several possibilities to enlarge these bounds, without any improvement. These results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.

Abstract:
Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one through the evolution. In this letter, we show a way of speedup in quantum adiabatic evolution algorithm, using the extended Hamiltonian. We present the exact relation between the energy gap and the elements of the extended Hamiltonian, which provides the new point of view to reduce the running time.

Abstract:
The impossibility of perfect cloning and state estimation are two fundamental results in Quantum Mechanics. It has been conjectured that quantum cloning becomes equivalent to state estimation in the asymptotic regime where the number of clones tends to infinity. We prove this conjecture using two known results of Quantum Information Theory: the monogamy of quantum correlations and the properties of entanglement breaking channels.

Abstract:
Quantum correlations as the resource for quantum communication can be distributed over long distances by quantum repeaters. In this Letter, we introduce the notion of a noisy quantum repeater, and examine its role in quantum communication. Quantum correlations shared through noisy quantum repeaters are then characterized and their secrecy properties are studied. Remarkably, noisy quantum repeaters naturally introduce private states in the key distillation scenario, and consequently key distillation protocols are demonstrated to be more tolerant.

Abstract:
A counter-intuitive result in entanglement theory was shown in [PRL 91 037902 (2003)], namely that entanglement can be distributed by sending a separable state through a quantum channel. In this work, following an analogy between the entanglement and secret key distillation scenarios, we derive its classical analog: secrecy can be distributed by sending non-secret correlations through a private channel. This strengthens the close relation between entanglement and secrecy.