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Abstract Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.
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Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
In this article, we consider a network of quantum sensors, where each sensor is a qubit detector that “fires,” i.e., its state changes when an event occurs close by. The change in state due to the firing of a detector is given by a unitary operator, which is the same for all sensors in the network. Such a network of detectors can be used to localize an event, using a protocol to determine the firing sensor, presumably the one closest to the event. The determination of the firing sensor can be posed as aQuantum State Discriminationproblem, which incurs a probability of error depending on the initial state and the measurement operators used. In this article, we address the problem of determining the optimal initial global state of a network of detectors that incur a minimum probability of error in determining the firing sensor. For this problem, we derive necessary and sufficient conditions for the existence of an initial state that allows for perfect discrimination, i.e., zero probability of error. Using insights from this result, we derive a conjectured optimal solution for the initial state, provide a pathway to prove the conjecture, and validate the conjecture empirically using multiple search heuristics that seem to perform near-optimally.
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- PAR ID:
- 10523559
- Publisher / Repository:
- Association for Computing Machinery
- Date Published:
- Journal Name:
- ACM Transactions on Quantum Computing
- Volume:
- 5
- Issue:
- 2
- ISSN:
- 2643-6809
- Page Range / eLocation ID:
- 1 to 25
- Subject(s) / Keyword(s):
- quantum sensor networks
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3655028
