Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. We also study quantum communication protocols in a more general context. We give a new protocol for the task of multiparty state merging. The previous multiparty state merging protocol required the use of time-sharing. Our protocol does not require time-sharing for distributed compression of two senders. In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. We illustrate the benefits of our approach by looking at different examples.
Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum entanglement, which can be exploited to achieve novel tasks such as teleportation and superdense coding. Current technologies allow the transmission of entangled photon pairs across distances up to roughly 100 kilometers. For longer distances, noise arising from various sources degrade the transmission of entanglement to the point that it becomes impossible to use the entanglement as a resource for future tasks. A strategy for dealing with this difficulty is to employ quantum repeaters, stations intermediate between the sender and receiver which participate in the process of entanglement distillation, thereby improving on what the sender and receiver could do on their own. In this work, we study entanglement distillation between two recipients sharing a mixed state and with the help of repeater stations. We extend the notion of entanglement of assistance to arbitrary states and give a protocol for extracting pure entanglement. We also study quantum communication protocols in a more general context. We give a new protocol for the task of multiparty state merging. The previous multiparty state merging protocol required the use of time-sharing. Our protocol does not require time-sharing for distributed compression of two senders. In the one-shot regime, we achieve multiparty state merging with entanglement costs not restricted to corner points of the entanglement cost region. Our analysis of the entanglement cost is performed using (smooth) min- and max-entropies. We illustrate the benefits of our approach by looking at different examples.
Motivated by the problem of designing quantum repeaters, we study entanglement distillation between two parties, Alice and Bob, starting from a mixed state and with the help of ``repeater'' stations. To treat the case of a single repeater, we extend the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibit a protocol, based on a random coding strategy, for extracting pure entanglement. The rates achievable by this protocol formally resemble those achievable if the repeater station could merge its state to one of Alice and Bob even when such merging is impossible. This rate is provably better than the hashing bound for sufficiently pure tripartite states. We also compare our assisted distillation protocol to a hierarchical strategy consisting of entanglement distillation followed by entanglement swapping. We demonstrate by the use of a simple example that our random measurement strategy outperforms hierarchical distillation strategies when the individual helper stations' states fail to individually factorize into portions associated specifically with Alice and Bob. Finally, we use these results to find achievable rates for the more general scenario, where many spatially separated repeaters help two recipients distill entanglement.
Bipartite qubit entanglement distillation is the process of converting noisy ebits into pure ebits using only local operations and classical communication. This is a core operation for quantum repeaters, enabling such crucial tasks as long-distance quantum communication and distributed quantum computing. In this work, we introduce a method for searching for entanglement distillation protocols and, using this technique, distil qubit Werner states at a higher rate than could be achieved using previously discovered protocols. In particular, we demonstrate the advantage of our new distillation strategy by improving the best-known lower bound for the two-way-assisted quantum capacity of the qubit depolarising channel across a wide range of channel parameters, making progress in one of the long-standing problems of quantum information theory.
We present a protocol for performing state merging when multiple parties share a single copy of a mixed state, and analyze the entanglement cost in terms of min- and max-entropies. Our protocol allows for interpolation between corner points of the rate region without the need for time-sharing, a primitive which is not available in the one-shot setting. We also compare our protocol to the more naive strategy of repeatedly applying a single-party merging protocol one party at a time, by performing a detailed analysis of the rates required to merge variants of the embezzling states. Finally, we analyze a variation of multiparty merging, which we call split-transfer, by considering two receivers and many additional helpers sharing a mixed state. We give a protocol for performing a split-transfer and apply it to the problem of assisted entanglement distillation.
Transmitting unknown quantum states to distant locations is crucial for distributed quantum information protocols. The seminal quantum teleportation scheme achieves this feat while requiring prior maximal entanglement between the sender and receiver. In scenarios with noisy entangled states, optimal teleportation fidelity characterizes the efficacy of transmitting the state, demanding the proper selection of local operations at the sender's and receiver's ends. The complexity escalates further in long-range communication setups, prompting the consideration of a repeater-based approach, which incorporates arrays of nodes with multiple segments to facilitate the efficient transmission of quantum information. The fidelity of the communication line gets degraded even if a single segment is affected by noise. In such cases, the general wisdom employs the standard entanglement swapping protocol involving maximally entangled states across the noiseless segments and applying maximally entangled basis measurement at the corresponding nodes to achieve optimal fidelity. In this Letter, we propose a more efficient protocol for a certain class of noisy states, achieving the same fidelity as the standard protocol while consuming less amount of entanglement. Our approach ensures optimal teleportation fidelity even when the end-to-end state gets noisier, and thus promises efficient utility of quantum resources in repeater-based distributed quantum protocols.
Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols: the two parties may be given some number of quantum bits jointly prepared in a fixed superposition, prior to communicating with each other. The quantum channel is then said to be "entanglement-assisted." Shared randomness does not help in the transmission of information from one party to another. Moreover, it does not significantly reduce the classical complexity of computing functions vis-a-vis private-coin protocols. On the other hand, prior entanglement leads to startling phenomena such as "quantum teleportation" and "superdense coding." The problem of characterising the power of prior entanglement has baffled many researchers, especially in the setting of bounded-error protocols. It is open whether it leads to more than a factor of two savings (using superdense coding) or more than an additive O(log) savings (when used to create shared randomness). Few lower bounds are known for communication problems in this setting, and are all derived using sophisticated information theoretic techniques. In this paper, we focus on the most basic problem in the setting of communication over an entanglement-assisted quantum channel, that of communicating classical bits from one party to another. We derive optimal bounds on the number of quantum bits required for this task, for any given probability of error.