Dong Pyo Chi

CONVEX-ROOF EXTENDED NEGATIVITY AS AN ENTANGLEMENT MEASURE FOR BIPARTITE QUANTUM SYSTEMS

We extend the concept of negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and classical communication, and derive explicit formulas for the entanglement measure of isotropic states and Werner states, applying the formalism presented by Vollbrecht and Werner [Phys. Rev. A 64, 062307 (2001)].

Quantum Database Search by a Single Query

In this paper we give a quantum mechanical algorithm that can search a database by a single query when the number of solutions is more than a quarter. It utilizes the generalized Grover operator of arbitrary phase.

Entanglement for a two-parameter class of states in 2 ⊗ n quantum system

We exhibit a two-parameter class of states ρ(α,γ) in a 2 ⊗ n quantum system for n ≥ 3, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral operations on a 2 ⊗ n quantum system. We calculate the negativity of ρ(α,γ), and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of ρ(α,γ) cannot exceed its negativity.

Initialization-free generalized Deutsch-Jozsa algorithm

We generalize the Deutsch-Jozsa algorithm by exploiting summations of the roots of unity. The generalized algorithm distinguishes a wider class of functions promised to be either constant or many to one and onto an evenly spaced range. As previously, the generalized quantum algorithm solves this problem using a single functional evaluation. We also consider the problem of distinguishing constant and evenly balanced functions and present a quantum algorithm for this problem that does not require any initialization of an auxiliary register involved in the process of functional evaluation and after solving the problem recovers the initial state of an auxiliary register.

Concurrence of assistance and Mermin inequality on three-qubit pure states

We study a relation between the concurrence of assistance and the Mermin inequality on three-qubit pure states and claim that if a three-qubit pure state has a minimal concurrence of assistance greater than 1/2 then the state violates some Mermin inequality. In this work, we analytically show that our claim holds for several classes and also find that it can be generalized to the set of all three-qubit pure states by exploiting previous numerical work [C. Emary and C. W. J. Beenakker, Phys. Rev. A 69, 032317 (2004)].

Quantum states for perfectly secure secret sharing

In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.

Bound entangled states with a nonzero distillable key rate

We present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005)] have nonzero distillable key rate and finally exhibit new classes of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of the distillable key rate for the classical-classical-quantum (ccq) states of their privacy squeezed versions, which represent the states after the local measurement performed in the key part without considering the shield part.

Monogamy equality in 2⊗2⊗d quantum systems

There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman–Kundu–Wootters inequality [Phys. Rev. A 61, 052306 (2000); Coffman–Kundu–WoottersPhys. Rev. Lett. 96, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, CA(BC)2=CAB2+(CACa)2, in the three-qubit system. In this paper, we consider the monogamy equality in 2⊗2⊗d quantum systems. We show that CA(BC)=CAB if and only if CACa=0 and also show that if CA(BC)=CACa, then CAB=0, while there exists a state in a 2⊗2⊗d system such that CAB=0 but CA(BC)>CACa.

Quantum functional oracles

The limitation on the size of quantum computers makes it important to reuse qubits for auxiliary registers even though they are entangled with others and are occupied by other computational processes. We construct a quantum algorithm that performs the functional phase rotation, which is the generalized form of the conventional conditional phase transforms, using the functional evaluation oracle. The constructed algorithm works without any a priori knowledge of the state of an auxiliary register at the beginning and it recovers the initial state of an auxiliary register at the end. This provides ample scope to choose qubits for auxiliary registers at will.

A SYNTHESIS OF RLC CIRCUITS FOR ARBITRARY WAVEFORM GENERATION

We consider an electrical network in which the series of resistor, inductor and capacitor are connected in parallel. When the finite measurements of the current are given, we present a method to construct an RLC circuit which generates the current fitting the measurements. This method will be useful to synthesize the voltage (or current) source of an arbitrary waveform which is necessary in the measurement of damage of a semiconductor device caused by an electrostatic discharge.