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Physical Review A

Local quantum measurement discrimination

Douglas F. Mundarain, Miguel Orszag

Published Jan 12, 2007• 6 citations
Publisher

Abstract

We study a scheme for a local quantum measurement discrimination, i.e., the estimation via local measurements on $B$ of previous measurements done in $A$ for a composed bipartite system $AB$. The common bath plays a crucial role in the process.

DOI
10.1103/physreva.75.012107

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The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. We first introduce two quantities called the spectral PPT-distance and relative spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show these quantities are related to the entanglement cost of optimal discrimination by PPT POVMs. Following this, we establish bounds and develop SDP hierarchies to estimate the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging these results, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
We study the performance of single-qubit probes for temperature estimation in the presence of collective baths. We consider a system of two qubits, each locally dissipating into its own bath while being coupled to a common bath. In this setup, we investigate different scenarios for temperature estimation of both the common and local baths. First, we explore how the precision of a single-qubit probe for estimating the common bath temperature can be enhanced by collective effects arising from the shared bath itself, particularly when the second qubit is in resonance with the probe. Interestingly, we find that the presence of local baths on each qubit can either jeopardize or, if these baths are sufficiently cold, enhance this precision. Next, we demonstrate a remote temperature sensing scheme in which one qubit acts as a probe to estimate the temperature of a local bath affecting the other qubit, by leveraging their indirect interaction through the common bath. This approach enables remote temperature sensing without directly coupling the probe to the target qubit or its local environment, thereby minimizing potential disturbances and practical challenges. Notably, we show that the collective Lamb shift, induced by the common bath, plays a crucial role in enabling remote temperature sensing by generating qubit-qubit correlations, even in the case of noninteracting qubits.
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