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\n  \n 2024\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n \n On the Duality of Teleportation and Dense Coding.\n \n \n \n \n\n\n \n Chitambar, E.; and Leditzky, F.\n\n\n \n\n\n\n IEEE Transactions on Information Theory, 70(5): 3529-3537. 5 2024.\n \n\n\n\n
\n\n\n\n \n \n \"OnPaper\n  \n \n \n \"OnWebsite\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{\n title = {On the Duality of Teleportation and Dense Coding},\n type = {article},\n year = {2024},\n pages = {3529-3537},\n volume = {70},\n websites = {https://ieeexplore.ieee.org/document/10315956/},\n month = {5},\n publisher = {Institute of Electrical and Electronics Engineers Inc.},\n id = {57c8a593-4166-303d-b1e9-cda19b598ac7},\n created = {2025-04-12T17:34:36.430Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T17:39:09.759Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially depends on the quality of the pre-shared entanglement. In this work, we revisit the problem of using noisy entanglement for the task of teleportation. We first show how this problem can be rephrased as a state discrimination problem. In this picture, a quantitative duality between teleportation and dense coding emerges in which every Alice-to-Bob teleportation protocol can be repurposed as a Bob-to-Alice dense coding protocol, and the quality of each protocol can be measured by the success probability in the same state discrimination problem. One of our main results provides a complete characterization of the states that offer no advantage in one-way teleportation protocols over classical states, thereby offering a new and intriguing perspective on the long-standing open problem of identifying such states. This also yields a new proof of the known fact that bound entangled states cannot exceed the classical teleportation threshold. Moreover, our established duality between teleportation and dense coding can be used to show that the exact same states are unable to provide a non-classical advantage for dense coding as well. We also discuss the duality from a communication capacity point of view, deriving upper and lower bounds on the accessible information of a dense coding protocol in terms of the fidelity of its associated teleportation protocol. A corollary of this discussion is a simple proof of the previously established fact that bound entangled states do not provide any advantage in dense coding.},\n bibtype = {article},\n author = {Chitambar, Eric and Leditzky, Felix},\n doi = {10.1109/TIT.2023.3331821},\n journal = {IEEE Transactions on Information Theory},\n number = {5}\n}
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\n Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially depends on the quality of the pre-shared entanglement. In this work, we revisit the problem of using noisy entanglement for the task of teleportation. We first show how this problem can be rephrased as a state discrimination problem. In this picture, a quantitative duality between teleportation and dense coding emerges in which every Alice-to-Bob teleportation protocol can be repurposed as a Bob-to-Alice dense coding protocol, and the quality of each protocol can be measured by the success probability in the same state discrimination problem. One of our main results provides a complete characterization of the states that offer no advantage in one-way teleportation protocols over classical states, thereby offering a new and intriguing perspective on the long-standing open problem of identifying such states. This also yields a new proof of the known fact that bound entangled states cannot exceed the classical teleportation threshold. Moreover, our established duality between teleportation and dense coding can be used to show that the exact same states are unable to provide a non-classical advantage for dense coding as well. We also discuss the duality from a communication capacity point of view, deriving upper and lower bounds on the accessible information of a dense coding protocol in terms of the fidelity of its associated teleportation protocol. A corollary of this discussion is a simple proof of the previously established fact that bound entangled states do not provide any advantage in dense coding.\n
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\n \n\n \n \n \n \n \n \n Information carried by a single particle in quantum multiple-access channels.\n \n \n \n \n\n\n \n Chen, X.; Zhang, Y.; Winter, A.; Lorenz, V., O.; and Chitambar, E.\n\n\n \n\n\n\n Physical Review A, 109(6). 6 2024.\n \n\n\n\n
\n\n\n\n \n \n \"InformationPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{\n title = {Information carried by a single particle in quantum multiple-access channels},\n type = {article},\n year = {2024},\n volume = {109},\n month = {6},\n publisher = {American Physical Society},\n day = {1},\n id = {1e57e60a-3245-3b4a-b633-2716de8ef5f5},\n created = {2025-04-12T18:16:49.740Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T18:16:50.862Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Nonclassical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how well multiparty information can be transmitted to a single receiver using just one classical or quantum particle. Our approach is based on a multiple-access communication model in which messages can be encoded into a single particle that is coherently distributed across multiple spatial modes. Theoretically, we derive lower bounds on the accessible information in the quantum setting that strictly separate it from the classical scenario. This separation is found whenever there is more than one sender, and also when there is just a single sender who has a shared phase reference with the receiver. When there is only one sender, the separation is impossible without a shared phase reference due to the famous Holevo's bound. Experimentally, we present a proof-of-principle demonstration of such quantum advantage in single-particle communication by implementing a multiport interferometer with messages being encoded along the different trajectories. Specifically, we consider a two-sender communication protocol built by a three-port optical interferometer. In this scenario, the rate sum achievable with a classical particle is upper bounded by one bit, while we experimentally observe a rate sum of 1.0152±0.0034 bits in the quantum setup.},\n bibtype = {article},\n author = {Chen, Xinan and Zhang, Yujie and Winter, Andreas and Lorenz, Virginia O. and Chitambar, Eric},\n doi = {10.1103/PhysRevA.109.062420},\n journal = {Physical Review A},\n number = {6}\n}
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\n Nonclassical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how well multiparty information can be transmitted to a single receiver using just one classical or quantum particle. Our approach is based on a multiple-access communication model in which messages can be encoded into a single particle that is coherently distributed across multiple spatial modes. Theoretically, we derive lower bounds on the accessible information in the quantum setting that strictly separate it from the classical scenario. This separation is found whenever there is more than one sender, and also when there is just a single sender who has a shared phase reference with the receiver. When there is only one sender, the separation is impossible without a shared phase reference due to the famous Holevo's bound. Experimentally, we present a proof-of-principle demonstration of such quantum advantage in single-particle communication by implementing a multiport interferometer with messages being encoded along the different trajectories. Specifically, we consider a two-sender communication protocol built by a three-port optical interferometer. In this scenario, the rate sum achievable with a classical particle is upper bounded by one bit, while we experimentally observe a rate sum of 1.0152±0.0034 bits in the quantum setup.\n
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\n \n\n \n \n \n \n \n \n The Communication Value of a Quantum Channel.\n \n \n \n \n\n\n \n Chitambar, E.; George, I.; Doolittle, B.; and Junge, M.\n\n\n \n\n\n\n IEEE Transactions on Information Theory, 69(3): 1660-1679. 3 2023.\n \n\n\n\n
\n\n\n\n \n \n \"ThePaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
\n 
@article{\n title = {The Communication Value of a Quantum Channel},\n type = {article},\n year = {2023},\n keywords = {Quantum information science,quantum channels,quantum entanglement},\n pages = {1660-1679},\n volume = {69},\n month = {3},\n publisher = {Institute of Electrical and Electronics Engineers Inc.},\n day = {1},\n id = {310e8db6-d5a9-3322-bbc0-9be25cbeac25},\n created = {2025-04-12T17:33:34.791Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T17:37:10.316Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).},\n bibtype = {article},\n author = {Chitambar, Eric and George, Ian and Doolittle, Brian and Junge, Marius},\n doi = {10.1109/TIT.2022.3218540},\n journal = {IEEE Transactions on Information Theory},\n number = {3}\n}
\n
\n\n\n
\n There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).\n
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\n \n\n \n \n \n \n \n \n Inferring Quantum Network Topology Using Local Measurements.\n \n \n \n \n\n\n \n Chen, D., T.; Doolittle, B.; Larson, J.; Saleem, Z., H.; and Chitambar, E.\n\n\n \n\n\n\n PRX Quantum, 4(4). 10 2023.\n \n\n\n\n
\n\n\n\n \n \n \"InferringPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
\n 
@article{\n title = {Inferring Quantum Network Topology Using Local Measurements},\n type = {article},\n year = {2023},\n volume = {4},\n month = {10},\n publisher = {American Physical Society},\n day = {1},\n id = {cb1762cc-7839-3ed5-8589-6cef35399984},\n created = {2025-04-12T17:35:28.004Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T18:11:21.439Z},\n read = {true},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities - namely, the von Neumann entropy and the measured mutual information - as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.},\n bibtype = {article},\n author = {Chen, Daniel T. and Doolittle, Brian and Larson, Jeffrey and Saleem, Zain H. and Chitambar, Eric},\n doi = {10.1103/PRXQuantum.4.040347},\n journal = {PRX Quantum},\n number = {4}\n}
\n
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\n Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities - namely, the von Neumann entropy and the measured mutual information - as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.\n
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\n \n\n \n \n \n \n \n \n Building Multiple Access Channels with a Single Particle.\n \n \n \n \n\n\n \n Zhang, Y.; Chen, X.; and Chitambar, E.\n\n\n \n\n\n\n Quantum, 6. 2022.\n \n\n\n\n
\n\n\n\n \n \n \"BuildingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{\n title = {Building Multiple Access Channels with a Single Particle},\n type = {article},\n year = {2022},\n volume = {6},\n publisher = {Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},\n id = {40387c84-bbac-3385-b75c-027eb3b896a8},\n created = {2025-04-12T17:33:24.424Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T18:11:07.691Z},\n read = {true},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {A multiple access channel describes a situation in which multiple senders are trying to forward messages to a single receiver using some physical medium. In this paper we consider scenarios in which this medium consists of just a single classical or quantum particle. In the quantum case, the particle can be prepared in a superposition state thereby allowing for a richer family of encoding strategies. To make the comparison between quantum and classical channels precise, we introduce an operational framework in which all possible encoding strategies consume no more than a single particle. We apply this framework to an Nport interferometer experiment in which each party controls a path the particle can traverse. When used for the purpose of communication, this setup embodies a multiple access channel (MAC) built with a single particle. We provide a full characterization of the Nparty classical MACs that can be built from a single particle, and we show that every quantum particle can generate a MAC outside the classical set. To further distinguish the capabilities of a single classical and quantum particle, we relax the locality constraint and allow for joint encodings by subsets of 1 < K ≤ N parties. This generates a richer family of classical MACs whose polytope dimension we compute. We identify a "generalized fingerprinting inequality" as a valid facet for this polytope, and we verify that a quantum particle distributed among N separated parties can violate this inequality even when K = N-1. Connections are drawn between the single-particle framework and multi-level coherence theory. We show that every pure state with K-level coherence can be detected in a semi-device independent manner, with the only assumption being conservation of particle number.},\n bibtype = {article},\n author = {Zhang, Yujie and Chen, Xinan and Chitambar, Eric},\n doi = {10.22331/Q-2022-02-16-653},\n journal = {Quantum}\n}
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\n A multiple access channel describes a situation in which multiple senders are trying to forward messages to a single receiver using some physical medium. In this paper we consider scenarios in which this medium consists of just a single classical or quantum particle. In the quantum case, the particle can be prepared in a superposition state thereby allowing for a richer family of encoding strategies. To make the comparison between quantum and classical channels precise, we introduce an operational framework in which all possible encoding strategies consume no more than a single particle. We apply this framework to an Nport interferometer experiment in which each party controls a path the particle can traverse. When used for the purpose of communication, this setup embodies a multiple access channel (MAC) built with a single particle. We provide a full characterization of the Nparty classical MACs that can be built from a single particle, and we show that every quantum particle can generate a MAC outside the classical set. To further distinguish the capabilities of a single classical and quantum particle, we relax the locality constraint and allow for joint encodings by subsets of 1 < K ≤ N parties. This generates a richer family of classical MACs whose polytope dimension we compute. We identify a \"generalized fingerprinting inequality\" as a valid facet for this polytope, and we verify that a quantum particle distributed among N separated parties can violate this inequality even when K = N-1. Connections are drawn between the single-particle framework and multi-level coherence theory. We show that every pure state with K-level coherence can be detected in a semi-device independent manner, with the only assumption being conservation of particle number.\n
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\n \n\n \n \n \n \n \n \n Certifying the classical simulation cost of a quantum channel.\n \n \n \n \n\n\n \n Doolittle, B.; and Chitambar, E.\n\n\n \n\n\n\n Physical Review Research, 3(4). 12 2021.\n \n\n\n\n
\n\n\n\n \n \n \"CertifyingPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{\n title = {Certifying the classical simulation cost of a quantum channel},\n type = {article},\n year = {2021},\n volume = {3},\n month = {12},\n publisher = {American Physical Society},\n day = {1},\n id = {32ded485-02b4-3d62-9f3c-a531f368e844},\n created = {2025-04-12T18:12:58.114Z},\n file_attached = {true},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-12T18:12:59.324Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the minimum amount of classical communication needed to perfectly simulate a channel's input-output correlations when unlimited shared randomness is held between encoder and decoder. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel. Among them, a single family of tests is shown to determine when a noisy classical channel can be simulated using an amount of communication strictly less than either its input or its output alphabet size. In addition, a family of eight signaling dimension witnesses is presented that completely characterize when any four-outcome measurement channel, such as a Bell measurement, can be simulated using one communication bit and shared randomness. Finally, we bound the signaling dimension for all partial replacer channels in d dimensions. The bounds are found to be tight for the special case of the erasure channel.},\n bibtype = {article},\n author = {Doolittle, Brian and Chitambar, Eric},\n doi = {10.1103/PhysRevResearch.3.043073},\n journal = {Physical Review Research},\n number = {4}\n}
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\n A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the minimum amount of classical communication needed to perfectly simulate a channel's input-output correlations when unlimited shared randomness is held between encoder and decoder. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel. Among them, a single family of tests is shown to determine when a noisy classical channel can be simulated using an amount of communication strictly less than either its input or its output alphabet size. In addition, a family of eight signaling dimension witnesses is presented that completely characterize when any four-outcome measurement channel, such as a Bell measurement, can be simulated using one communication bit and shared randomness. Finally, we bound the signaling dimension for all partial replacer channels in d dimensions. The bounds are found to be tight for the special case of the erasure channel.\n
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\n \n\n \n \n \n \n \n Bounds on Instantaneous Nonlocal Quantum Computation.\n \n \n \n\n\n \n Gonzales, A.; and Chitambar, E.\n\n\n \n\n\n\n IEEE Transactions on Information Theory, 66(5). 2020.\n \n\n\n\n
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@article{\n title = {Bounds on Instantaneous Nonlocal Quantum Computation},\n type = {article},\n year = {2020},\n keywords = {Quantum entanglement,quantum computing,teleportation},\n volume = {66},\n id = {4b98f2fe-0dd1-3232-b018-f4fb720aa631},\n created = {2025-04-13T16:50:14.501Z},\n file_attached = {false},\n profile_id = {889ca0d7-cd8b-3818-bafe-550deb56f3f0},\n group_id = {deeee398-84e9-3f66-b6a1-20d512cc898d},\n last_modified = {2025-04-13T16:50:14.501Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 1963-2012 IEEE. Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with $\\epsilon $ -error using $O(\\log (1/\\epsilon))$ entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as $O(1/\\epsilon)$. We also consider the family of binary controlled gates on dimensions $d_A\\otimes d_B$. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of $\\log d_B$ ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when $d_A=2$. This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.},\n bibtype = {article},\n author = {Gonzales, A. and Chitambar, E.},\n doi = {10.1109/TIT.2019.2950190},\n journal = {IEEE Transactions on Information Theory},\n number = {5}\n}
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\n © 1963-2012 IEEE. Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with $\\epsilon $ -error using $O(\\log (1/\\epsilon))$ entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as $O(1/\\epsilon)$. We also consider the family of binary controlled gates on dimensions $d_A\\otimes d_B$. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of $\\log d_B$ ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when $d_A=2$. This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.\n
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