Ultimate limits of approximate unambiguous discrimination
- URL: http://arxiv.org/abs/2010.15753v1
- Date: Thu, 29 Oct 2020 16:58:42 GMT
- Title: Ultimate limits of approximate unambiguous discrimination
- Authors: Quntao Zhuang
- Abstract summary: Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision is allowed to vanish any possibility of errors when a conclusive result is obtained.
In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels.
For the special class of teleportation-covariant' channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.
- Score: 1.14219428942199
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum hypothesis testing is an important tool for quantum information
processing. Two main strategies have been widely adopted: in a minimum error
discrimination strategy, the average error probability is minimized; while in
an unambiguous discrimination strategy, an inconclusive decision (abstention)
is allowed to vanish any possibility of errors when a conclusive result is
obtained. In both scenarios, the testing between quantum states are relatively
well-understood, for example, the ultimate limits of the performance are
established decades ago; however, the testing between quantum channels is less
understood. Although the ultimate limit of minimum error discrimination between
channels has been explored recently, the corresponding limit of unambiguous
discrimination is unknown. In this paper, we formulate an approximate
unambiguous discrimination scenario, and derive the ultimate limits of the
performance for both states and channels. In particular, in the channel case,
our lower bound of the inconclusive probability holds for arbitrary adaptive
sensing protocols. For the special class of `teleportation-covariant' channels,
the lower bound is achievable with maximum entangled inputs and no adaptive
strategy is necessary.
Related papers
- Discrimination of bosonic dephasing quantum channels [3.7498611358320733]
We study the possibility of discriminating between two bosonic dephasing quantum channels.
In the presence of an input energy constraint, we derive an upper bound on the error probability.
We extend these results from single-shot to multi-shot discrimination, envisaging the behavior.
arXiv Detail & Related papers (2024-07-20T17:01:03Z) - Semantic Strengthening of Neuro-Symbolic Learning [85.6195120593625]
Neuro-symbolic approaches typically resort to fuzzy approximations of a probabilistic objective.
We show how to compute this efficiently for tractable circuits.
We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles.
arXiv Detail & Related papers (2023-02-28T00:04:22Z) - Experimental quantum state discrimination using the optimal fixed rate
of inconclusive outcomes strategy [0.0]
We experimentally investigate the strategy for the optimal discrimination of two non-orthogonal states considering a fixed rate of inconclusive outcomes (FRIO)
We present a versatile experimental scheme that performs the optimal FRIO measurement for any pair of generated non-orthogonal states with arbitrary a priori probabilities and for any fixed rate of inconclusive outcomes.
arXiv Detail & Related papers (2022-04-14T01:18:50Z) - Enhanced discrimination of high-dimensional quantum states by
concatenated optimal measurement strategies [0.0]
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory.
We experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the unambiguous optimal strategy.
We achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions.
arXiv Detail & Related papers (2021-12-18T22:19:05Z) - Experimental multi-state quantum discrimination through a Quantum
network [63.1241529629348]
We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information.
The first protocol achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver.
arXiv Detail & Related papers (2021-07-21T09:26:48Z) - Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing [87.17253904965372]
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies.
We show that these errors decrease exponentially with decay rates given by the measured relative entropies between the two states.
arXiv Detail & Related papers (2021-04-30T00:52:48Z) - Minimax Off-Policy Evaluation for Multi-Armed Bandits [58.7013651350436]
We study the problem of off-policy evaluation in the multi-armed bandit model with bounded rewards.
We develop minimax rate-optimal procedures under three settings.
arXiv Detail & Related papers (2021-01-19T18:55:29Z) - 'Interaction-Free' Channel Discrimination [0.0]
We generalize the notion of 'interaction-free' measurement to arbitrary quantum channels.
Our main result is a necessary and sufficient criterion for when it is possible or impossible to discriminate quantum channels in an 'interaction-free' manner.
arXiv Detail & Related papers (2020-10-01T18:06:56Z) - On Lower Bounds for Standard and Robust Gaussian Process Bandit
Optimization [55.937424268654645]
We consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm.
We provide a novel proof technique for deriving lower bounds on the regret, with benefits including simplicity, versatility, and an improved dependence on the error probability.
arXiv Detail & Related papers (2020-08-20T03:48:14Z) - Discrimination of Ohmic thermal baths by quantum dephasing probes [68.8204255655161]
We evaluate the minimum error probability achievable by three different kinds of quantum probes, namely a qubit, a qutrit and a quantum register made of two qubits.
A qutrit probe outperforms a qubit one in the discrimination task, whereas a register made of two qubits does not offer any advantage.
arXiv Detail & Related papers (2020-08-06T08:51:51Z) - Ultimate limits for multiple quantum channel discrimination [0.966840768820136]
This paper studies the problem of hypothesis testing with quantum channels.
We establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels.
We also show that this lower bound is achievable when the channels have certain symmetries.
arXiv Detail & Related papers (2020-07-29T03:08:48Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.