arXiv subjects

Yonghae Lee

Publications and source records attributed to Yonghae Lee.

11 recordsLinked to original sources

arXiv2026

Three-Qubit State Preparation: Classification and Explicit Circuits

We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a $1|2$ bipartition. Given a target state specified by its amplitudes, we provide concrete criteria and concurrence-based tests that determine its type. For each type, we derive an explicit circuit template composed of elementary single-qubit rotations and CNOT gates, with gate parameters determined systematically from the Schmidt decomposition. The full construction is described step by step from the target amplitudes, with no procedural ambiguity. As an application, we further group frequently encountered three-qubit pure states in quantum information into four classes and provide an explicit circuit for each class. Compared with prior approaches, our circuits are designed for practical use: they admit a direct algorithmic instantiation, use only CNOT gates between adjacent qubits, and for certain classes achieve smaller gate counts and circuit depth.

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arXiv2025

Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm

We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus on lower-order phase components, and the punctured method removes qubits corresponding to known phase bits, thereby streamlining the circuit. To demonstrate the effectiveness of the two variations, we integrate them into a hybrid quantum-classical implementation of the Harrow--Hassidim--Lloyd algorithm for solving linear systems. The hybrid method leverages both quantum and classical processors to identify and remove unnecessary qubits and gates. As a result, our method reduces qubit and gate counts compared to previous implementations, leading to lower overall circuit error rates on current hardware. Experimental demonstrations on IBM superconducting hardware confirm the error-mitigation effectiveness of the proposed hybrid method.

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arXiv2025

Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions

We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and extend them to two orthogonal pure states. For three mutually orthogonal states, we provide formulas for specific cases and discuss the challenges of obtaining analytic expressions for the rest. Additionally, we derive explicit formulas for certain orthonormal bases and analyze those containing one or two maximally entangled states. Finally, we prove that no orthonormal basis can consist of three product states and one entangled state.

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arXiv2024

Improved bounds on quantum uncommon information

In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages required to be exchanged to completely share all information in common. However, this equivalence does not extend to quantum information theory. Specifically, quantum uncommon information is operationally defined as the minimal amount of entanglement required for the quantum communication task of quantum state exchange, where two parties exchange quantum states to share all quantum messages in common. Currently, an analytical closed-form expression for the quantum uncommon information remains undetermined. In this work, by investigating underlying characterization of the quantum uncommon information, we derive improved bounds on it. To obtain these bounds, we develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. We also consider a referee-assisted exchange, wherein a referee aids two parties in efficiently performing the quantum state exchange. Our bounds provide more precise estimations for the quantum uncommon information. Furthermore, we demonstrate that the subspace technique is a versatile tool for characterizing uncommon information not only in the bipartite scenario but also in various multi-partite ones.

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arXiv2023

The necessary and sufficient conditions when global and local fidelities are equal

In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system $A \otimes B$ is always less than or equal to the quantum fidelity between the states in subsystem $A$ alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system $A \otimes B$ and subsystem $A$, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results.

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arXiv2021

Quantum state rotation: Circularly transferring quantum states of multiple users

Quantum state exchange is a quantum communication task for two users in which the users faithfully exchange their respective parts of an initial state under the asymptotic scenario. In this work, we generalize the quantum state exchange task to a quantum communication task for $M$ users in which the users circularly transfer their respective parts of an initial state. We assume that every pair of users may share entanglement resources, and they use local operations and classical communication in order to perform the task. We call this generalized task the (asymptotic) quantum state rotation. First of all, we formally define the quantum state rotation task and its optimal entanglement cost, which means the least amount of total entanglement required to carry out the task. We then present lower and upper bounds on the optimal entanglement cost, and provide conditions for zero optimal entanglement cost. Based on these results, we find out a difference between the quantum state rotation task for three or more users and the quantum state exchange task.

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arXiv2019

One-shot quantum state exchange

The quantum state exchange is a quantum communication task in which two users exchange their respective quantum information in the asymptotic setting. In this work, we consider a one-shot version of the quantum state exchange task, in which the users hold a single copy of the initial state, and they exchange their parts of the initial state by means of entanglement-assisted local operations and classical communication. We first derive lower bounds on the least amount of entanglement required for carrying out this task, and provide conditions on the initial state such that the protocol succeeds with zero entanglement cost. Based on these results, we reveal two counter-intuitive phenomena in this task, which make it different from a conventional SWAP operation. One tells how the users deal with their symmetric information in order to reduce the entanglement cost. The other shows that it is possible for the users to gain extra shared entanglement after this task.

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arXiv2018

State exchange with quantum side information

We consider a quantum communication task between two users Alice and Bob, in which Alice and Bob exchange their respective quantum information by means of local operations and classical communication assisted by shared entanglement. Here, we assume that Alice and Bob may have quantum side information, not transferred, and classical communication is free. In this work, we derive general upper and lower bounds for the least amount of entanglement which is necessary to perfectly perform this task, called the state exchange with quantum side information. Moreover, we show that the optimal entanglement cost can be negative when Alice and Bob make use of their quantum side information. We finally provide conditions on the initial state for the state exchange with quantum side information which give the exact optimal entanglement cost.

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arXiv2018

Quantum secret sharing and Mermin operator

Quantum secret sharing is well known as a method for players to share a classical secret for secret sharing in quantum mechanical ways. Most of the results associated with quantum secret sharing are based on pure multipartite entangled states. In reality, however, it is difficult for players to share a pure entangled state, although they can share a state close to the state. Thus, it is necessary to study how to perform the quantum secret sharing based on a general multipartite state. We here present a quantum secret sharing protocol on an $N$-qubit state close to a pure $N$-qubit Greenberger-Horne-Zeilinger state. In our protocol, $N$ players use an inequality derived from the Mermin inequality to check secure correlation of classical key bits for secret sharing. We show that if our inequality holds then every legitimate player can have key bits with positive key rate. Therefore, for sufficiently many copies of the state, the players can securely share a classical secret with high probability by means of our protocol.

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arXiv2018

Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience

We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation algorithm to reduce a circuit depth from the original HHL algorithm. In this paper, we show that this hybrid algorithm is functionally identical to the HHL algorithm under the assumption that the number of qubits used in algorithms is large enough. In addition, it is experimentally examined with four qubits in the IBM Quantum Experience setups, and the experimental results of our algorithm show higher accurate performance on specific systems of linear equations than that of the HHL algorithm.

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arXiv2018

State transfer with quantum side information

We first consider quantum communication protocols between a sender Alice and a receiver Bob, which transfer Alice's quantum information to Bob by means of non-local resources, such as classical communication, quantum communication, and entanglement. In these protocols, we assume that Alice and Bob may have quantum side information, not transferred. In this work, these protocols are called the state transfer with quantum side information. We determine the optimal costs for non-local resources in the protocols, and study what the effects of the use of quantum side information are. Our results can give new operational meanings to the quantum mutual information and the quantum conditional mutual information, which directly provide us with an operational interpretation of the chain rule for the quantum mutual information.

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