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arXiv:2201.00388 · Journal of Physics A Mathematical and Theoretical

Discrimination of dephasing channels

Milajiguli Rexiti, Laleh Memarzadeh, Stefano Mancini

Published May 5, 2022• 8 citations
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Abstract

Abstract The problem of dephasing channel discrimination is addressed for finite-dimensional systems. In particular, the optimization with respect to input states without energy constraint is solved analytically for qubit, qutrit and ququart. Additionally, it is shown that resorting to side entanglement assisted strategy is completely useless in this case.

DOI
10.1088/1751-8121/ac6d2c

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Abstract The problem of dephasing channel discrimination is addressed for finite-dimensional systems. In particular, the optimization with respect to input states without energy constraint is solved analytically for qubit, qutrit and ququart. Additionally, it is shown that resorting to side entanglement assisted strategy is completely useless in this case.
Abstract We address the issue of the discrimination between two-qubit amplitude damping channels by exploring several strategies. For the single-shot, we show that the excited state does not always give the optimal input, and that side entanglement assistance has limited benefit. On the contrary, feedback assistance from the environment is more beneficial. For the two-shot, we prove the in-utility of entangled inputs. Then focusing on individual (local) measurements, we find the optimal adaptive strategy.
A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of ddd states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.
Entanglement is known to be a powerful resource that improves performance in various quantum information and computational tasks. A standard example of such a phenomenon is the possibility of perfectly discriminating all four Pauli operations in a single shot via the superdense coding protocol. While entanglement is often a powerful resource for quantum channel discrimination, this is not necessarily the case. In this work, we identify scenarios in which the maximally entangled state is a bad choice of input state and, more generally, show that excessive entanglement can reduce channel discriminability dramatically. To do so, we present an explicit pair of unitary channels which are perfectly discriminable without entanglement, but for which any strategy with maximally entangled input states is εεε-close to a blind uniform guessing strategy. To develop a systematic approach, we introduce the concepts of Maximal Entanglement Worst Case (MEWC) and Maximal Entanglement Best Case (MEBC) pairs of channels, and present conditions for a pair of channels to be MEWC or MEBC. With these conditions, we show that the optimal input states for discriminating MEWC pairs of channels are necessarily separable, and provide non-trivial examples of measurement channels for which entanglement necessarily reduces the maximum probability of discrimination.
Distinguishing one quantum channel from another becomes a next natural question following the advent of quantum state discrimination. Here, we address the problem of quantum channel discrimination with the separable states and the entangled states input. Two schemes, based on the simulator for quantum networks and channels framework (SQUANCH) and the quantum machine learning toolbox (QMLT), are proposed to perform the quantum channel discrimination task. In the first scheme, we give an example of several qubit channels, verify that the performance metrics of channel discrimination can be improved by the entangled states. In the second scheme, we train a quantum circuit learning model to classify quantum channels using the Adam stochastic optimization algorithm. Although we consider the distinguishability in the case of only two possible channels, this model can be extended to any number of channels. This method can provide a good solution for distinguishing some complex quantum channels.