arXiv subjects

Soojoon Lee

Publications and source records attributed to Soojoon Lee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements

Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. The quantum coherence of a quantum measurement can be converted into the entanglement in a bipartite quantum measurement through coherence-non generating transformations. Conversely, a quantum entanglement monotone of quantum measurements induces a quantum coherence monotone of quantum measurement. Our results confirm that the understanding on the link between quantum coherence and quantum entanglement is valid even for quantum measurements which do not generate any quantum resource.

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arXiv2021

Quantum algorithm based on the $\varepsilon$-random linear disequations for the continuous hidden shift problem

There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we define the continuous hidden shift problem on $\mathbb{R}^n$ with a continuous oracle function as an extension of the hidden shift problem, and also define the $\varepsilon$-random linear disequations which is a generalization of the random linear disequations. By employing the newly defined concepts, we show that there exists a quantum computational algorithm which solves this problem in time polynomial in $n$.

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arXiv2021

Quantum cryptographic resource distillation and entanglement

We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing.

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arXiv2021

One-Shot Static Entanglement Cost of Bipartite Quantum Channels

We first investigate the one-shot static entanglement cost to simulate a bipartite quantum channel under the set of non-entangling channels. The lower bound on the static entanglement cost is given by the generalized robustness of the target channel as well as the robust-generating power of the channel, which implies that the cost necessary to generate a bipartite quantum channel might not be retrievable in general. Next, we conceive a set of quantum channels that extends the set of non-entangling channels. We find out that the one-shot static entanglement cost under the extended set of channels is given by the channel's standard log-robustness. This gives the one-shot dynamic entanglement cost under a set of free superchannels that do not generate dynamic entanglement resource; the extended set is shown to be equivalent to the set of free superchannels.

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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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arXiv2020

One-shot manipulation of entanglement for quantum channels

We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesis-testing relative entropy of channels with minimization over separable channels. We also address the one-shot catalytic dynamic entanglement cost of a bipartite quantum channel under a larger class of free superchannels that could generate the dynamic entanglement which is asymptotically negligible; it is bounded by the generalized log-robustness of channels.

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arXiv2020

Genuine Secret-Sharing States

Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if $N$ players share an $N$-party genuine secret-sharing state, then arbitrary $M$ players out of the total players can share an $M$-party genuine secret-sharing state by means of local operations and classical communication on the state. We also define the distillable rate with respect to the genuine secret-sharing state, and explain the connection between the distillable rate and the relative entropy of entanglement.

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arXiv2020

Generalization of port-based teleportation and controlled teleportation capability

As a variant of the original quantum teleportation, the port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of the ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of the controlled port-based teleportation by combining the controlled teleportation with the port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present new quantities called the control power and the minimal control power for the new controlled version on a given tripartite quantum state.

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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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arXiv2019

Upper bounds on the quantum capacity for general attenuator and amplifier

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.

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arXiv2019

Activation and superactivation of single-mode Gaussian quantum channels

Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low. This means that we can transmit quantum information reliably through very noisy Gaussian channels having zero quantum capacity. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the non-activation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.

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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

Activation of quantum capacity of Gaussian channels

Quantum channels can be activated by a kind of channels whose quantum capacity is zero. This activation effect might be useful to overcome noise of channels by attaching other channels which can enhance the capacity of a given channel. In this work, we show that such an activation is possible by specific positive-partial-transpose channels for Gaussian lossy channels whose quantum capacities are known. We also test more general case involving Gaussian thermal attenuator whose the exact value of quantum capacity has been unknown so far. For a recently suggested narrow upper bound on quantum capacity of the thermal attenuator, we confirm the fact that an activation of quantum capacity occurs as well. This result is applicable for realistic situations in which Gaussian channels describe the noises of communication systems.

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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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arXiv2018

Conditional quantum entropy power inequality for $d$-level quantum systems

We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert, Datta, and Ozols [J. Math. Phys. 57, 052202 (2016)]. Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.

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arXiv2018

Correspondence between maximally entangled states in discrete and Gaussian regimes

We study a general corresponding principle between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) states via quantum purification method. In the previous work, we have already investigated an information-theoretic correspondence between the Gaussian maximally mixed states (GMMSs) and their purifications known as Gaussian maximally entangled states (GMESs) in [Phys. Lett. A {\bf 380}, 3607 (2016)]. We here compare an $N\times N$-dimensional maximally entangled state to the GMES we proposed previously, through an explicit calculation of quantum fidelity between those entangled states. By exploiting the results, we naturally conclude that our GMES is more suitable to the concept of \emph{maximally entangled} state in Gaussian quantum information, and thus it might be useful or applicable for quantum information tasks than the two-mode squeezed vacuum (TMSV) state in the Gaussian regime.

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