{"uid":"cap_l4v60JaZ3coAxR38bs7l5","slug":"observable-expectation-values-pauli-x-y-z-for-single-qubit-density-3e32779c","name":"Observable Expectation Values — Pauli X, Y, Z for Single-Qubit Density Matrix","description":"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.","url":"https://www.mahastrategies.com/api/v1/compute/quantum/observable-expectations?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"state":{"type":"object"},"dataClass":{"enum":["public","synthetic"],"type":"string"}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.016003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.016003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.016003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.016003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_BBNZbNqnAc2ZhT0YBn8rq","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.016003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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).","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Bloch vector extraction for qubit state","prompt":"I have a qubit density matrix [[0.6, 0.3], [0.3, 0.4]] and I need to know its Bloch sphere coordinates — can you compute the X, Y, and Z Pauli expectation values for it? Mark the data as public."},{"title":"Verifying quantum channel output","prompt":"After applying a depolarizing channel to my qubit, the output state is [[0.5, 0.05-0.05i], [0.05+0.05i, 0.5]]. Can you compute the Pauli X, Y, and Z expectations so I can confirm the channel reduced the Bloch vector as expected? Data class is synthetic."},{"title":"Quantum simulation state diagnostics","prompt":"I'm running a simulation and at each time step I have a single-qubit density matrix. For the current step the state is [[0.8, 0.2i], [-0.2i, 0.2]] — give me the X, Y, and Z observable expectations so I can track how the state evolves. The data is synthetic."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-15T06:39:28.905Z","isFirstParty":false,"canonicalSlug":"observable-expectation-values-pauli-x-y-z-for-single-qubit-density-3e32779c"}