Near-term large quantum computers are not able to operate as a single processing unit. It is therefore required to partition a quantum circuit into smaller parts, and then each part is executed on a small unit. This approach is known as distributed quantum computation. In this study, a dynamic programming algorithm is proposed to minimize the number of communications in a distributed quantum circuit (DQC). This algorithm consists of two steps: first, the quantum circuit is converted into a bipartite graph model, and then a dynamic programming approach (DP) is proposed to partition the model into low-capacity quantum circuits. The proposed approach is evaluated on some benchmark quantum circuits with remarkable reduction in the number of required teleportations.
In many quantum information processing protocols, entangled states shared among parties are an important resource. In this article, we study how bipartite states may be distributed in the context of a quantum network limited by timing constraints. We explore various tasks that plausibly arise in this context, and characterize the achievability of several of these in settings where only one-way communication is allowed. We provide partial results in the case where two-way communication is allowed. This builds on earlier work on summoning single and bipartite systems.
We show how branching spin chains can be used to both generate and distribute entanglement from their natural dynamics. Such entanglement provides a useful resource, for example for teleportation or distributed quantum processing. Once distributed, this resource can be isolated through mapping or swapping the entanglement into specific qubits at the ends of branches. Alternatively, as we demonstrate for distributed bipartite entanglement, applying simple single-qubit operations to the end spin of one or more branches can dynamically freeze the entanglement at the branch ends.
A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising sim…
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as Robust Semidefinite Programs (RSDP). We propose, using well known properties of RSDP, several new sufficient tests for the separability of mixed states. Our results are then generalized to multipartite density operators.
We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.
We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified with the degree of separability of the state. In a recent work, the problem was solved for two-qubit states using semidefinite programming. In this paper, we describe a procedure to obtain the optimal decomposition of a bipartite state of any finite dimension via a sequence of semidefinite relaxations. The sequence of decompositions thus obtained is shown to c…
We present a detailed investigation of minimum detection efficiencies, below which locality cannot be violated by any quantum system of any dimension in bipartite Bell experiments. Lower bounds on these minimum detection efficiencies are determined with the help of linear programming techniques. Our approach is based on the observation that any possible bipartite quantum correlation originating from a quantum state in an arbitrary dimensional Hilbert space is sandwiched between two probability polytopes, namely the local (Bell) polytope and a corresponding nonlocal no-signaling polytope. Numer…
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to dis…
We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. In the problem we address, the output of Alice's measurement can be infinite or contin…
Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes assisted zero-error quantum capacity depends only on the non-commutative bipartite graph of the channel and the one-shot case can be computed efficiently by semidefinite programming (SDP). As an example, the activated PPTp codes assisted zero-error quantum capacity is carefully studied. We then present a general SDP upper bound $Q_Γ$ of quantum capacity and show it is always…
Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and ap…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. These methods extend with fabric growth while scaling linearly in time and quadratically in footprint. We also provide methods for handling hard faults in the logical fabric without invoking approximations to the origin…
Distributing entanglement among multiple users is a fundamental problem in quantum networks, requiring an efficient solution. In this work, a protocol is proposed for extracting maximally entangled (GHZn) states for any number of parties in quantum networks of arbitrary topology. It is based on the graph state formalism and requires minimal assumptions on the network state. The protocol only requires local measurements at the network nodes and just a single qubit memory per user. Existing protocols on bipartite entanglement routing are also improved for specific nearest-neighbor network archit…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. For synchronous correlations, we show a correspondence between the minimal entanglement dimension and the completely positive sem…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an operational interpretation as a guessing probability when one of the subsystems is classical. We then show that the extended conditional min-entropy can be used to fully characterize when two bipartite quantum channels are related to each other via a superchannel (also known as supermap or a comb) that is acting on one of the subsystems. This relation is a pre-orde…
The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing local unitary dynamics. The problems are related to the geometric measure of entanglement and the distillability problem. We show that the problems can be reduced to semi-definite programming optimization problems. We give close-form formulae of the fidelity when the two states are both pure states, or a pure product state and the Werner state. We explain from t…
