Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1608.07461

A Four-Round LOCC Protocol Outperforms All Two-Round Protocols in Reducing the Entanglement Cost for A Distributed Quantum Information Processing

Eyuri Wakakuwa, Akihito Soeda, Mio Murao

Published Aug 26, 2016• 5 citations
arXivHTMLPDF

Abstract

We prove that there is a trade-off relation between the entanglement cost and the number of rounds of communication, for two distant parties to accomplish a bidirectional quantum information task by local operations and classical communication (LOCC). We consider an implementation of a class of two-qubit controlled-unitary gate by LOCC assisted by shared entanglement, in an information theoretical scenario of asymptotically many input pairs and vanishingly small error. We prove the trade-off relation by showing that one ebit of entanglement per pair is necessary to be consumed for implementing the unitary by any two-round protocol, whereas the entanglement cost by a four-round protocol is strictly smaller than one ebit per pair.

DOI
10.48550/arxiv.1608.07461

Related papers

Complexity of Causal Order Structure in Distributed Quantum Information Processing: More Rounds of Classical Communication Reduce Entanglement Cost

Eyuri Wakakuwa, Akihito Soeda, Mio Murao

We prove a trade-off relation between the entanglement cost and classical communication round complexity of a protocol in implementing a class of two-qubit unitary gates by two distant parties, a key subroutine in distributed quantum information processing. The task is analyzed in an information theoretic scenario of asymptotically many input pairs with a small error that is required to vanish sufficiently quickly. The trade-off relation is shown by (i) one ebit of entanglement per pair is necessary for implementing the unitary by any two-round protocol, and (ii) the entanglement cost by a three-round protocol is strictly smaller than one ebit per pair. We also provide an example of bipartite unitary gates for which there is no such trade-off.

arXiv:1810.08447•Physical Review Letters•May 16, 2019•15 citations

A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation

Eyuri Wakakuwa, Akihito Soeda, Mio Murao

We analyze implementations of bipartite unitaries by means of local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in the quantum Shannon theory to study an asymptotic scenario, in which two distant parties perform the same bipartite unitary on infinitely many pairs of inputs. We analyze minimum cost of entanglement and classical communication per copy. For two-round LOCC protocols, we derive a single-letter formula for the minimum cost of entanglement and classical communication, under an additional requirement that the error converges to zero faster than 1/n4, where n is the number of input pairs. The formula is given by the “Markovianizing cost” of a tripartite state associated with the unitary, which can be computed by a finite-step algorithm. We also derive a lower bound on the minimum cost of resources, which applies for protocols with arbitrary number of rounds.

arXiv:1505.04352•IEEE Transactions on Information Theory•May 29, 2017•18 citations

A coding theorem for bipartite unitaries in distributed quantum computation

Eyuri Wakakuwa, Akihito Soeda, Mio Murao

We analyze implementations of bipartite unitaries in a distributed quantum computation setting using local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in quantum Shannon theory to study an asymptotic scenario in which the two distant parties perform the same bipartite unitary on infinitely many pairs of input states generated by a completely random i.i.d. (independent and identically distributed) quantum information source. We analyze the minimum costs of resources of entanglement and classical communication per copy. For protocols consisting of two-round LOCC, we prove that an achievable rate tuple of costs of entanglement and classical communication is given by the “Markovianizing cost” of a tripartite state associated with the unitary, which is conjectured to be optimal as well. The Markovianizing cost can be computed by a finite-step algorithm.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•6 citations

Information Theoretical Analysis of Distributed Quantum Computation

若桑, 江友里

Distributed quantum computation is a task in which many distant parties perform a large quantum computation in collaboration with each other, by using classical communication, quantum communication or shared entanglement as resources.In this thesis, we consider one of the simplest nontrivial task of distributed quantum computation, that is, implementation of bipartite unitary by LOCC (local operations and classical communication) assisted by shared entanglement.Here, two input states are distributed over two distant parties.Contrary to previous researches, we consider an asymptotic scenario in which the two parties perform the same bipartite unitary on infinitely many independent input pairs.We analyze the minimum amount of resources required for the task by exploiting concepts and techniques developed in the field of quantum Shannon theory, which has originally been developed to analyze quantum communication.As a tool for analyzing distributed quantum computation, we first introduce a task that we call Markovianization.Markovianization is a task in which a tripartite pure state is transformed to a state called quantum Markov chain, by a randomizing operation on one of the three subsystems.We derive the minimum cost of randomness required for Markovianization (Markovianizing cost) by exploiting a novel decomposition of a Hilbert space introduced in the context of quantum cryptography.We then apply the obtained result to distributed quantum computation.We mainly consider implementation of bipartite unitaries by entanglement-assisted LOCC protocols consisting of three steps, called one-round protocols.This is the first nontrivial case because it is not possible to implement bipartite unitaries by protocols consisting of only one or two steps.Our main result is that we derive the minimum costs of entanglement and classical communication.We show that the minimum costs are given by the Markovianizing cost of a tripartite state associated with the unitary.The result indicates that information about input states of computation is divided into three components: one of which only information of amplitude in a basis is required for computation (information of phase is not), another of which both amplitude and phase information are required, and the other of which no information is involved in computation.Our construction of a protocol that requires the smallest amount of resources is based on this decomposition.We also propose a method to compute the Markovianizing cost of a state associated with the unitary.We also consider two-round protocols, that is, protocols consisting of concatenation of two one-round protocols, for two-qubit controlled unitaries.We show that, for a particular class of two-qubit controlled unitaries, the minimum entanglement cost in two-round protocols is strictly smaller than that in one-round protocols.This result is the first reported case that indicates a property of a trade-off relation between entanglement requirement and the number of turns in entanglement-assisted LOCC tasks.The research in this thesis opens a possibility to build a new bridge between quantum computation theory and quantum communication theory, which are the two largest subfield of quantum information theory, by analyzing a problem in the former using concepts and techniques developed in the latter.

•Mar 24, 2015•0 citations

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

Guangkuo Liu, Ian M. George, Eric Chitambar

A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity.

arXiv:2204.00781•Quantum•Sep 7, 2023•4 citations

More assistance of entanglement, less rounds of classical communication

Atanu Bhunia, Indranil Biswas, Indrani Chattopadhyay +1 more

Abstract Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this paper, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in d ⊗ d , which require at least 2 d − 2 round of classical communications. Curiously the round number can be reduced to d by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistance.

arXiv:2303.13645•Journal of Physics A Mathematical and Theoretical•Aug 7, 2023•7 citations
We prove that there is a trade-off relation between the entanglement cost and the number of rounds of communication, for two distant parties to accomplish a bidirectional quantum information task by local operations and classical communication (LOCC). We consider an implementation of a class of two-qubit controlled-unitary gate by LOCC assisted by shared entanglement, in an information theoretical scenario of asymptotically many input pairs and vanishingly small error. We prove the trade-off relation by showing that one ebit of entanglement per pair is necessary to be consumed for implementing the unitary by any two-round protocol, whereas the entanglement cost by a four-round protocol is strictly smaller than one ebit per pair.
We prove a trade-off relation between the entanglement cost and classical communication round complexity of a protocol in implementing a class of two-qubit unitary gates by two distant parties, a key subroutine in distributed quantum information processing. The task is analyzed in an information theoretic scenario of asymptotically many input pairs with a small error that is required to vanish sufficiently quickly. The trade-off relation is shown by (i) one ebit of entanglement per pair is necessary for implementing the unitary by any two-round protocol, and (ii) the entanglement cost by a three-round protocol is strictly smaller than one ebit per pair. We also provide an example of bipartite unitary gates for which there is no such trade-off.
We analyze implementations of bipartite unitaries by means of local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in the quantum Shannon theory to study an asymptotic scenario, in which two distant parties perform the same bipartite unitary on infinitely many pairs of inputs. We analyze minimum cost of entanglement and classical communication per copy. For two-round LOCC protocols, we derive a single-letter formula for the minimum cost of entanglement and classical communication, under an additional requirement that the error converges to zero faster than 1/n4, where n is the number of input pairs. The formula is given by the “Markovianizing cost” of a tripartite state associated with the unitary, which can be computed by a finite-step algorithm. We also derive a lower bound on the minimum cost of resources, which applies for protocols with arbitrary number of rounds.
We analyze implementations of bipartite unitaries in a distributed quantum computation setting using local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in quantum Shannon theory to study an asymptotic scenario in which the two distant parties perform the same bipartite unitary on infinitely many pairs of input states generated by a completely random i.i.d. (independent and identically distributed) quantum information source. We analyze the minimum costs of resources of entanglement and classical communication per copy. For protocols consisting of two-round LOCC, we prove that an achievable rate tuple of costs of entanglement and classical communication is given by the “Markovianizing cost” of a tripartite state associated with the unitary, which is conjectured to be optimal as well. The Markovianizing cost can be computed by a finite-step algorithm.
Distributed quantum computation is a task in which many distant parties perform a large quantum computation in collaboration with each other, by using classical communication, quantum communication or shared entanglement as resources.In this thesis, we consider one of the simplest nontrivial task of distributed quantum computation, that is, implementation of bipartite unitary by LOCC (local operations and classical communication) assisted by shared entanglement.Here, two input states are distributed over two distant parties.Contrary to previous researches, we consider an asymptotic scenario in which the two parties perform the same bipartite unitary on infinitely many independent input pairs.We analyze the minimum amount of resources required for the task by exploiting concepts and techniques developed in the field of quantum Shannon theory, which has originally been developed to analyze quantum communication.As a tool for analyzing distributed quantum computation, we first introduce a task that we call Markovianization.Markovianization is a task in which a tripartite pure state is transformed to a state called quantum Markov chain, by a randomizing operation on one of the three subsystems.We derive the minimum cost of randomness required for Markovianization (Markovianizing cost) by exploiting a novel decomposition of a Hilbert space introduced in the context of quantum cryptography.We then apply the obtained result to distributed quantum computation.We mainly consider implementation of bipartite unitaries by entanglement-assisted LOCC protocols consisting of three steps, called one-round protocols.This is the first nontrivial case because it is not possible to implement bipartite unitaries by protocols consisting of only one or two steps.Our main result is that we derive the minimum costs of entanglement and classical communication.We show that the minimum costs are given by the Markovianizing cost of a tripartite state associated with the unitary.The result indicates that information about input states of computation is divided into three components: one of which only information of amplitude in a basis is required for computation (information of phase is not), another of which both amplitude and phase information are required, and the other of which no information is involved in computation.Our construction of a protocol that requires the smallest amount of resources is based on this decomposition.We also propose a method to compute the Markovianizing cost of a state associated with the unitary.We also consider two-round protocols, that is, protocols consisting of concatenation of two one-round protocols, for two-qubit controlled unitaries.We show that, for a particular class of two-qubit controlled unitaries, the minimum entanglement cost in two-round protocols is strictly smaller than that in one-round protocols.This result is the first reported case that indicates a property of a trade-off relation between entanglement requirement and the number of turns in entanglement-assisted LOCC tasks.The research in this thesis opens a possibility to build a new bridge between quantum computation theory and quantum communication theory, which are the two largest subfield of quantum information theory, by analyzing a problem in the former using concepts and techniques developed in the latter.
A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity.
Abstract Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this paper, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in d ⊗ d , which require at least 2 d − 2 round of classical communications. Curiously the round number can be reduced to d by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistance.