# Observable Expectation Values — Pauli X, Y, Z for Single-Qubit Density Matrix

> Observable Expectation Values — Pauli X, Y, Z for Single-Qubit Density Matrix is a paid API for AI agents from www.mahastrategies.com, paid per call via x402, $0.016003/call, status unknown (last checked 2026-10-15).

Computes the X, Y, and Z Pauli observable expectation values for a supplied single-qubit density matrix, returning results with basis conventions (not a hardware measurement).

## Facts

- Endpoint: POST https://www.mahastrategies.com/api/v1/compute/quantum/observable-expectations?utm_source=zero.xyz
- Price: $0.016003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/observable-expectation-values-pauli-x-y-z-for-single-qubit-density-3e32779c
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_l4v60JaZ3coAxR38bs7l5

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability observable-expectation-values-pauli-x-y-z-for-single-qubit-density-3e32779c -d '<json body>'
```

Example prompt: Calculate the Pauli X, Y, and Z expectation values for my single-qubit density matrix — the state is [[0.7, 0.1+0.2i], [0.1-0.2i, 0.3]] and the data class is synthetic.

## When to prefer this

Use this endpoint when you need fast, analytically exact Pauli expectation values for a single-qubit density matrix without access to quantum hardware. It is ideal for simulation diagnostics, Bloch vector extraction, and verification of quantum channel outputs. Prefer this over hardware-based measurement services when you need deterministic, noise-free results at low cost per call.

## Known failure modes

- Invalid or non-physical density matrix (not Hermitian, trace not equal to 1, or negative eigenvalues) returns an error
- Malformed state object schema causes a 400 bad request
- Unsupported dataClass value outside the allowed enum returns a validation error
- Payment not fulfilled (x402 protocol) results in a 402 response and no computation
- Network timeout on large or malformed state objects

## How this service works

Calculate X, Y and Z Pauli expectations for a supplied valid single-qubit density matrix. Returns basis conventions; not a hardware measurement. New modular adapter: retained result recovery for 24 hours, minimal receipt metadata for 90 days. Existing live route unchanged.

## Output

Returns the computed expectation values ⟨X⟩, ⟨Y⟩, and ⟨Z⟩ of the three Pauli operators for the supplied density matrix, along with the basis conventions used. Results are retained for 24 hours; minimal receipt metadata is kept for 90 days. This is a purely analytical computation, not a hardware measurement.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "state": {
   "type": "object"
  },
  "dataClass": {
   "enum": [
    "public",
    "synthetic"
   ],
   "type": "string"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/observable-expectation-values-pauli-x-y-z-for-single-qubit-density-3e32779c/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from www.mahastrategies.com](https://www.zero.xyz/host/www.mahastrategies.com/llms.txt)