Distributed quantum operations need both quantum resources and classical coordination. Sending ordinary circuit requests to several independent processors is one form of distributed workflow, but it does not create entanglement between them. A protocol that consumes shared entanglement has additional requirements involving pair generation, storage, synchronization, and the interpretation of measurement results.
This chapter uses constructed arithmetic and established protocol ideas. The local Bell and memory laboratories do not simulate a deployed quantum network, certify an interconnect, or demonstrate remote hardware execution. Their evidence habits remain useful: define the resource, record its context, and distinguish physical events from interpreted success.
Define the resource being delivered
An elementary entanglement service might attempt to create a pair shared by two endpoints and report a heralding event. That event signals success under the protocol's detection model. It does not automatically establish a perfect Bell pair. Loss, detector behavior, preparation errors, and other mechanisms affect the conditional state.
A useful record identifies endpoints, attempt and pair identifiers, creation or herald times, the relevant phase/frame information, and the validity conditions for use. Quality estimates must specify how they were established. Measuring every usable pair to reconstruct its state would generally consume the resource being delivered; quality is typically assessed through models and appropriate characterization or test samples.
Memory introduces another constraint. A pair created early may wait while another link succeeds or while classical coordination finishes. Its usefulness can change during that wait. A resource count without age and quality context can therefore overstate what is available to a protocol.
Teleportation consumes resources and needs communication
In the standard qubit teleportation protocol, the sender and receiver first share entanglement. The sender jointly measures the input and its half of the pair, producing classical information that lets the receiver determine the appropriate correction or frame interpretation. The ideal protocol consumes the input at the sender and the shared pair; it does not leave an additional copy of an unknown state. Bennett and colleagues' original protocol establishes this combination of resources.
The receiver needs the classical measurement information to recover the intended usable state. Entanglement therefore does not provide faster-than-light messaging. Classical propagation and processing remain part of the operating schedule, even when some corrections can be tracked in a frame instead of immediately applied.
Entanglement swapping can connect more distant endpoints by consuming shorter-range pairs and performing intermediate operations. The resulting quality and availability depend on those input pairs, measurements, and their coordination. A longer route cannot be assessed solely by adding nominal link bandwidths.
Worked example: average availability is not a deadline
Consider a synthetic elementary link with independent attempts, success probability 0.2 per attempt, and one millisecond per complete attempt including its herald. Assume no memory expiry. The expected number of attempts to first success is 1 / 0.2 = 5, giving a mean of five milliseconds.
That mean is not a five-millisecond delivery guarantee. The probability of at least one success in k attempts is 1 − 0.8^k. After five attempts it is 0.67232. Reaching at least 99 percent success for this single-link model requires 21 attempts, since 0.8^21 is below 0.01 while 0.8^20 is not.
Now suppose a protocol needs two independent links, each attempted in parallel with these same assumptions. Both are ready by five attempts with probability 0.67232², approximately 0.452014. Earlier pairs must also survive the wait for their partners; the calculation assumed away that additional constraint. These numbers describe a constructed model, not measured network performance.
Coordinate consumption explicitly
A scheduler must distinguish an attempted pair, a heralded pair, a reserved pair, and a consumed or expired pair. Classical retries need to preserve that distinction. A repeated control message should not cause the same quantum resource to be assigned to two consumers, and a lost acknowledgment should not be interpreted as proof that a consumed resource remains available.
Keep the classical record and physical-resource interpretation connected, including the limits of what can be recovered after failure. Classical logs can be replayed; an unknown quantum state cannot generally be reconstructed from those logs. Protocol recovery may require generating new entanglement and restarting an affected operation.
Exercise: review a service promise
A team measures a mean elementary-link delivery time near five milliseconds and promises that a two-link protocol completes within five milliseconds 99 percent of the time. Does the synthetic model support the promise?
Answer. No. Even with independent links, no expiry, and no extra coordination cost, both links are ready within five attempts only about 45.2 percent of the time. A complete protocol also needs its operations and classical messages. Measure or model the appropriate end-to-end deadline distribution and resource lifetimes before making a service commitment.
The timing chapter provides the same distinction between average processing cost and a usable deadline guarantee inside one processor. Across a network, propagation, resource age, and coordination add further dependencies.