Trading Resources for Communication

Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the other hand, quantum protocol designers may commit much more faults than classical protocol designers since human intuition is much better adapted to the classical world than the quantum world. To offer formal techniques for modeling and verification of quantum protocols, several quantum extensions of process algebra have been proposed. One of the most serious issues in quantum process algebra is to discover a quantum generalization of the notion of bisimulation, which lies in a central position in process algebra, preserved by parallel composition in the presence of quantum entanglement, which has no counterpart in classical computation. Quite a few versions of bisimulation have been defined for quantum processes in the literature, but in the best case they are only proved to be preserved by parallel composition of purely quantum processes where no classical communications are involved. Many quantum cryptographic protocols, however, employ the LOCC (Local Operations and Classical Communications) scheme, where classical communications must be explicitly specified. So, a notion of bisimulation preserved by parallel composition in the circumstance of both classical and quantum communications is crucial for process algebra approach to verification of quantum cryptographic protocols. In this paper we introduce a novel notion of bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communications are present. We also establish some basic algebraic laws for this bisimulation. In particular, we prove uniqueness of the solutions to recursive equations of quantum processes, which provides a powerful proof technique for verifying complex quantum protocols.

We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor is it possible for the OR function itself in the exact case. This dichotomy naturally suggests a study of bounded-depth predicates (i.e. those in the polynomial hierarchy) between OR and MAJORITY. We present black-box algorithms that achieve near quadratic speed up for all such predicates.

We report successful joint operation of quantum and classical communications with shared hardware. Leveraging information learned from the classical DSP, low-noise quantum communications (0.009 SNU at 15 km) compatible with 15 Mbit/s QKD is demonstrated.

We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical communication, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.

We introduce an intermediate setting between quantum nonlocality and communication complexity problems. More precisely, we study the value of XOR games when Alice and Bob are allowed to use a limited amount (c bits) of one-way classical communication compared to their value when they are allowed to use the same amount of one-way quantum communication (c qubits). The key quantity here is the ratio between the quantum and classical value. We provide a universal way to obtain Bell inequality violations of general Bell functionals from XOR games for which the previous quotient is larger than 1. This allows, in particular, to find (unbounded) Bell inequality violations from communication complexity problems in the same spirit as the recent work by Buhrman et al. (PNAS 113(12):3191–3196, 2016). We also provide an example of a XOR game for which the previous quotient is optimal (up to a logarithmic factor) in terms of the amount of information c. Interestingly, this game has only polynomially many inputs per player. For the related problem of separating the classical versus quantum communication complexity of a function, the known examples attaining exponential separation require exponentially many inputs per party.

Suppose two distant observers, Alice and Bob, share some form of entanglement - quantum correlations - in some bipartite pure quantum states. They may apply local operations and classical communication to convert one form of entanglement to another. Since entanglement is regarded as a resource in quantum information processing, it is an important question to ask how much classical communication, which is also a resource, is needed in the inter-conversion process of entanglement. In this paper, we address this important question in the many-copy case. The inter-conversion process of entanglement is usually divided into two types: concentrating the entanglement from many partially entangled states into a smaller number of maximally entangled states (i.e., singlets) and the reverse process of diluting singlets into partially entangled states. It is known that entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of /spl radic/N. Our main result is to prove that this prior art result is optimal up to a constant factor; any procedure for approximately creating N partially entangled states from singlets requires /spl Omega/(/spl radic/N) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transformations. We also prove a lower bound on the inefficiency of the process: to dilute singlets to N copies of a partially entangled state, the entropy of entanglement must decrease by /spl Omega/(/spl radic/N). Moreover, we introduce two new tools - /spl delta/-significant subspaces and the standard form protocol reduction in entanglement manipulations. We hope that these two new tools will be useful in other work in quantum information theory.

Realizing long-distance quantum key distribution (QKD) in fiber channel where classical optical communications and quantum signals are multiplexed by their different wavelengths has attracted considerable attentions. The achievable secure distance of commonly-used Bennet-Brassard 1984 (BB84) protocol is lowered severely due to inevitable crosstalk from classical optical pulses. Unlike conventional quantum key distribution (QKD) protocols, round-robin differential-phase-shift (RRDPS) QKD protocol has a high tolerance for noise, since the potential information leakage in this protocol can be bounded without monitoring signal disturbance. Thus, it may be a promising protocol under noisy channel. In this work, we investigate the performance, e.g., achievable secure distance of RRPDS protocol, when crosstalk from classical communication is considered. Surprisingly, we find that RRPDS only has quite limited advantage over BB84 protocol when optical misalignment of QKD system is serious. If misalignment is trivial, BB84 can even outperform RRDPS protocol.

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Continuous variable quantum key distribution (CVQKD) based on a simultaneous quantum and classical communication (SQCC) protocol can use a single coherent communication system for multiple purposes. In this paper, we propose an inter-satellite SQCC-CVQKD scheme in the terahertz (THz) band. This scheme performs classical modulation at the sending end, followed by quantum Gaussian modulation operations. At the receiving end, an amplifier is used to amplify and demultiplex the received signal, and, finally, a homodyne detector or heterodyne detector is selected for decoding. We have demonstrated the security of the SQCC-CVQKD system in the THz band, and a performance analysis of the scheme is given in the finite-size regime. The simulation results show that this scheme has a higher secret key rate and stronger anti-interference ability in practice. This work provides an effective way to construct wireless quantum communication networks.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

This paper presents photonic communications and data storage capacitates for classical and quantum communications over a quantum channel. These capacities represent a generalization of Shannon’s classical channel capacity and coding theorem in two ways. First, it extends classical results for bit communication transport to all frequencies in the electromagnetic spectrum. Second, it extends the results to quantum bit (qubit) transport as well as a hybrid of classical and quantum communications. Nature’s limits on the rate at which classical and/or quantum information can be sent error-free over a quantum channel using classical and/or quantum error-correcting codes are presented as a function of the thermal background light level and Einstein zero-point energy. Graphical results are given as well as numerical results regarding communication rate limits using Planck’s natural frequency and time-interval units!

Quantum communication enables various technological possibilities that are hard or impossible with classical communication. These include secure distribution of keys, transfer of quantum information and distributed quantum computation and sensing. Quantum communication relies on the ability to transmit a quantum state over some distance. Exponential photon loss from fibre inevitably limits the distance one would be able to achieve this over and therefore make use of these promising new technologies.Quantum repeaters have been proposed as a solution to this problem. Elementary repeater protocols involve dividing the channel into smaller segments with repeater nodes, distributing entanglement between these nodes and then performing swapping operations to connect entangled pairs and purification to correct operation errors. In the years since these elementary protocols, quantum repeaters have been through extensive theoretical improvements including utilising the benefits of quantum error correction to improve efficiency.However, the vast majority of these protocols are for discrete encodings of quantum information. There is significant interest in using continuous variable encodings of quantum information for quantum communication applications. This is motivated in part by the ease of generating, manipulating and detecting quantum states and additionally the increased compatibility with existing infrastructure. In this thesis we present one of the first quantum repeater protocols for continuous variable encodings of quantum information.The continuous variable quantum repeater we present in this thesis is based on concatenated error correction protocols that work to correct loss on any optical field state. We thoroughly investigate operation of this error correction protocol including the trade-offs associated with real implementations, various modifications to the error correction protocol as well as whether it can be implemented with current technology.We illustrate how these error correction protocols may be structured to form a quantum repeater that inhibits the exponential photon loss problem with a resource cost that scales polynomially with distance. We show that our continuous variable repeater is able to beat the fundamental bound on quantum communication without a repeater. Finally, we compare the performance of our first generation continuous variable repeater to existing first generation discrete variable protocols.

We propose a passive continuous-variable quantum key distribution (CVQKD) protocol based on simultaneous quantum and classical communication (SQCC) under indoor environments and in inter-satellite links within the terahertz band. In our PSQCC-CVQKD scheme, classical modulation is performed at the transmitter, followed by passive quantum modulation operations. At the receiver, an amplifier is utilized to amplify and demultiplex the received signal, and a homodyne or heterodyne detector is subsequently selected for decoding. We derive the security bounds of the protocol and evaluate its performance in both indoor environments and inter-satellite links. Furthermore, by considering finite-size effects, we achieve tighter agreement constraints, which are more practical than those obtained in the asymptotic limit. Simulation results indicate that this scheme exhibits a high secret key rate and strong jamming resistance in practical applications, providing a more efficient pathway for the construction of future quantum networks.

Quantum network is a promising platform for numerous quantum applications, including distributed quantum computing, secure communication, and improved sensing. Implementing entanglement distribution between remote quantum nodes plays a vital role in realizing the quantum network's capabilities, and it requires effective remote entanglement distribution protocols. To meet this requirement, we propose two strategies, namely connection-oriented and connectionless, to achieve end-to-end entanglement distribution inspired by the designs of classical communication. For the connection-oriented strategy, an exclusive quantum connection is pre-established between the source and destination nodes. For the connectionless strategy, entanglement swapping is performed hop-by-hop tentatively. In this way, the best-effort service is provided for the source node to establish long-distance entanglement with the destination node. Analogous to classical communication, the proposed strategies have their advantages and disadvantages. Our simulation results show that the connectionless strategy is more efficient and robust than the connection-oriented strategy in terms of throughput. However, the connection-oriented strategy provides reliable end-to-end entanglement distribution but at the expense of higher overhead. Moreover, the application scenarios of these two strategies are discussed. This work paves the road for designing end-to-end entanglement distribution protocols in quantum networks.

Nonlocality is at the heart of quantum information processing. In this paper we investigate the minimum amount of classical communication required to simulate a nonlocal quantum measurement. We derive general upper bounds, which in turn translate to systematic classical simulations of quantum communication protocols.As a concrete application, we prove that any quantum communication protocol with shared entanglement for computing a Boolean function can be simulated by a classical protocol whose cost does not depend on the amount of the shared entanglement. This implies that if the cost of communication is a constant, quantum and classical protocols, with shared entanglement and shared coins, respectively, compute the same class of functions.Furthermore, we describe a new class of efficient quantum communication protocols based on fast quantum algorithms. While some of them have efficient classical simulations by our method, others appear to be good candidates for separating quantum v.s. classical protocols, and quantum protocols with v.s. without shared entanglement.Yet another application is in the context of simulating quantum correlations using local hidden variable models augmented with classical communications. We give a constant cost, approximate simulation of quantum correlations when the number of correlated variables is a constant, while the dimension of the entanglement and the number of possible measurements can be arbitrary.Our upper bounds are expressed in terms of some tensor norms on the measurement operator. Those norms capture the nonlocality of bipartite operators in their own way and may be of independent interest and further applications.