Abstract
An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.
Highlights
Entanglement is the key resource in quantum information processing that brings advantages over its classical counterparts
In quantum state fidelity estimation (QSFE), one evaluates expectation values of certain observables from the whole measurement outputs instead of testing each input by each output of measurements according to a “strategy”; we refer to the “strategy” in quantum state verification (QSV) as “state verifier operators” in the context of QSFE in this paper
We have employed state verifiers in Lemma 1 to derive lower and upper bounds on state fidelity in Lemma 2, which can be refined under the assistance of measurement statistics in the computational basis
Summary
Entanglement is the key resource in quantum information processing that brings advantages over its classical counterparts. To qualify an entanglement generation process, one will need to extract some information on the created states by measurements. For the qualification of a state generation process, instead of full QST, one may just need to employ quantum state fidelity estimation (QSFE) to reveal partial information about the most relevant Pauli operator components that signify the target state [16,17,18]. One can even ease the measurement complexity, if one just estimates the lower and upper bounds instead of the exact value of the state fidelity. Such an approach is employed in [19] for the detection of entanglement dimensionality in a higher-dimensional entanglement generation process
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