We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise model we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e. expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two-qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five-qubit linear cluster state and a Greenberger–Horne–Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained.
We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise model we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e. expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two-qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five-qubit linear cluster state and a Greenberger–Horne–Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained.
We present an entanglement generation scheme which allows arbitrary graph states to be efficiently created in a linear quantum register via an auxiliary entangling bus (EB). The dynamical evolution of the EB is described by an effective non-interacting fermionic system undergoing mirror-inversion in which qubits, encoded as local fermionic modes, become entangled purely by Fermi statistics. We discuss a possible implementation using two species of neutral atoms stored in an optical lattice and find that the scheme is realistic in its requirements even in the presence of noise.
How much noise can a given quantum state tolerate without losing its entanglement? For qudits of arbitrary dimension, I investigate this question for two noise models: Global white noise, where a depolarizing channel is applied to all qudits simultaneously, and local white noise, where a single qudit depolarizing channel is applied to every qudit individually. Using a unitary generalization of the Pauli group, I derive noise thresholds for stabilizer states, with an emphasis on graph states, and compare different entanglement criteria. The PPT and reduction criteria generally provide high noise thresholds, however, it is difficult to apply them in the case of local white noise. Entanglement criteria based on so-called sector lengths, on the other hand, provide coarse noise thresholds for both noise models. The only thing one has to know about a state to compute this threshold is the number of its full-weight stabilizers. In the special case of qubit graph states, I relate this question to a graph-theoretical puzzle and solve it for four important families of states. For Greenberger-Horne-Zeilinger states under local white noise, I obtain for the first time a noise threshold below which so-called semiseparability is ruled out.
We consider entanglement-based quantum networks, where multipartite entangled resource states are distributed and stored among the nodes and locally manipulated upon request to establish the desired target configuration. Separating the generation process from the requests enables a pre-preparation of resources, hence a reduced network latency. It also allows for an optimization of the entanglement topology, which is independent of the underlying network geometry. We concentrate on establishing Bell pairs or tripartite GHZ states between arbitrary parties. We study the influence of noise in this process, where we consider imperfections in state preparation, memories, and measurements - all of which can be modeled by local depolarizing noise. We compare different resource states corresponding to linear chains, trees, or multi-dimensional rectangular clusters, as well as centralized topologies using bipartite or tripartite entangled states. We compute the fidelity of the target states using a recently established efficient method, the noisy stabilizer formalism, and identify the best resource states within these classes. This allows us to treat networks of large size containing millions of nodes. We find that in large networks, high-dimensional cluster states are favorable and lead to a significantly higher target state fidelity.
I present a protocol that converts |E| elementary two-qubit resource states, one per edge of a target graph G=(V,E), into the distributed graph state |G> using only operations local to each party and classical communication, reaching arbitrary graph topologies rather than the GHZ class of prior walk-based schemes. The elementary step is obtained from the coined discrete-time quantum walk by replacing the position-permuting shift with a diagonal CZ gate, the phase quantum walk (PQW); on each edge it realises the entanglement-assisted non-local CZ gate. Because every gate and correction is diagonal, all edges run in a single round with the local correction C_v = Z_v^{g_v}, verified exhaustively on 22 connected graphs (32,212 outcomes) at F = 1.0. The central result is an exact fidelity theory under independent Pauli noise on the resource qubits, with a separate channel on each. When the noise acts after the local gate, the fidelity factorises over vertices; for depolarising noise F* = prod_v [1 + (1 - 4p/3)^{deg v}]/2, with the degree sequence entering only at second order. When it acts on the stored pair, as link-generation, transmission and storage noise does, it becomes an edge-cover partition function, F* = 2^{-|V|} sum_{S subset V} (1 - 4p/3)^{2|E(S)|}, bounded above by the vertex product and with a leading-order loss coefficient 3/2 times larger. Dephasing gives the same fidelity at both placements. On ibm_kingston, direct fidelity estimation certifies F = 0.815(3) for |L_4>, 0.776(3) for |GHZ_4> and 0.733(3) for |C_4>. Native SWAP-free execution at coupling girth gamma requires target girth at least gamma/3 and maximum degree at most 3; on heavy-hex this forbids triangles, though |K_4>, being LC-equivalent to a star, remains reachable.
Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the usefulness of graph states. We consider a noise model where the initial qubits, prepared in | + ⟩ states, undergo depolarizing noise before the application of the CZ operations that generate edges between qubits situated at the nodes of the resulting graph state. For this model we develop a method for calculating the coherent information – a lower bound on the rate at which entanglement can be distilled, across a bipartition of the graph state. We also identify some patterns on how adding more nodes or edges affects the bipartite distillable entanglement. As an application, we find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.
Coherence-to-entanglement conversion transforms single-qubit superposition into a practical two-qubit resource, but noise limits this process in near-term quantum hardware. We derive closed-form benchmarks for a minimal CNOT primitive in which a coherent qubit and an incoherent ancilla generate entanglement before undergoing phase damping, global depolarizing, amplitude damping, or independent local depolarizing noise. Using the ℓ1-norm of coherence and negativity, we prove the noiseless law N0=Cℓ1/2, valid for arbitrary mixed inputs, and obtain exact negativities, survival fractions, and entanglement-sudden-death thresholds. For all X-state-preserving channels, a master relation shows that entanglement loss results from the competition between coherence suppression and partial-transpose spectral shifts. Phase damping yields η=1−p without finite-noise sudden death; global depolarization gives coherence-dependent sudden death; amplitude damping adds an excited-population penalty and sudden death only for θ>π/4; while local depolarization is most destructive at equal depolarizing strength. The initial survival slopes, −1, −3/2, −2, and −3, act as compact noise fingerprints. Since concurrence satisfies C=2N for the generated states, all robustness rankings remain unchanged. Mapping channel parameters to T1, Tφ, and average gate fidelity connects the theory to hardware-level performance.