We propose a scheme for simultaneous classical communication and parameter estimation of generalized Pauli channels. This framework relies on the facts that i) under certain conditions, Pauli channels act as classical symmetric channel, and ii) a recently proposed parameter estimation method of Pauli channels can be executed while satisfying the conditions of i). The performance of the parameter estimation part in this simultaneous scheme relies on the symbol error rate of the communication module. This reliance gives rise to a natural tradeoff between the communication rate and the performance of parameter estimation in this simultaneous scheme. We exemplify our protocol by utilizing repetition codes for communication and the aforementioned parameter estimation scheme for the characterization of the channel at hand. We explore the tradeoff behavior between the communication rate and the performance of parameter estimation in the numerical examples. Our proposal paves the way for practical methods in simultaneous communication and channel estimation over unknown quantum channels.
We propose a scheme for simultaneous classical communication and parameter estimation of generalized Pauli channels. This framework relies on the facts that i) under certain conditions, Pauli channels act as classical symmetric channel, and ii) a recently proposed parameter estimation method of Pauli channels can be executed while satisfying the conditions of i). The performance of the parameter estimation part in this simultaneous scheme relies on the symbol error rate of the communication module. This reliance gives rise to a natural tradeoff between the communication rate and the performance of parameter estimation in this simultaneous scheme. We exemplify our protocol by utilizing repetition codes for communication and the aforementioned parameter estimation scheme for the characterization of the channel at hand. We explore the tradeoff behavior between the communication rate and the performance of parameter estimation in the numerical examples. Our proposal paves the way for practical methods in simultaneous communication and channel estimation over unknown quantum channels.
We consider the problem of estimating time-varying quantum noise. Specifically, we focus on Pauli qubit noise with time-variations and attempt to construct the most accurate instantaneous channel description. To this end, we propose an adaptive framework of simultaneous communication and parameter estimation (SCAPE) that efficiently and accurately estimates the time-varying Pauli channel while communicating reliably over the channel being estimated. This adaptive framework gives the informed control of communication rate–parameter estimation tradeoff to communicating parties. Interestingly, this adaptive SCAPE requires post-processing entirely on the receiver’s end and minimal feedback to the sender to increase, decrease, or continue with the same code rate of employed error correcting code. This procedure can be particularly useful in time-varying quantum channels with natural periodic deviations in channel conditions, e.g., in satellite communication channels.
To capture the problem of joint communication and sensing in the quantum regime, we consider the problem of reliably communicating over a Classical-Quantum (c-q) channel that depends on a random parameter while simultaneously estimating the random parameter at the transmitter through a noisy feedback channel. Specifically, for non-adaptive estimation strategies, we obtain an exact characterization of the optimal tradeoffs between the rate of communication and the error exponent of parameter estimation. As in the classical setting, the tradeoff is governed by the empirical distribution of the codewords, which simultaneously controls the rate of reliable communication and the error exponent.
We propose a parameter estimation protocol for generalized Pauli channels acting on d -dimensional Hilbert space. The salient features of the proposed method include product probe states and measurements, the number of measurement configurations linear in d , minimal post-processing, and the scaling of the mean square error comparable to that of the entanglement-based parameter estimation scheme for generalized Pauli channels. We also show that while measuring generalized Pauli operators the errors caused by the Pauli noise can be modeled as measurement errors. This makes it possible to utilize the measurement error mitigation framework to mitigate the errors caused by the generalized Pauli channels. We use this result to mitigate noise on the probe states and recover the scaling of the noiseless probes, except with a noise strength-dependent constant factor. This method of modeling Pauli channel as measurement noise can also be of independent interest in other NISQ tasks, e.g., state tomography problems, variational quantum algorithms, and other channel estimation problems where Pauli measurements have the central role.
This article explores the performance of quantum communication systems in the presence of noise and focuses on finding the optimal encoding for maximizing the classical communication rate, approaching the classical capacity in some scenarios. Instead of theoretically bounding the ultimate capacity of the channel, we adopt a signal processing perspective to estimate the achievable performance of a physically available but otherwise unknown quantum channel. By employing a variational algorithm to estimate the trace distance between quantum states, we numerically determine the optimal encoding protocol for the amplitude damping and Pauli channels. Our simulations demonstrate the convergence and accuracy of the method with a few iterations, confirming that optimal conditions for binary quantum communication systems can be variationally determined with minimal computation. Furthermore, since the channel knowledge is not required at the transmitter or at the receiver, these results can be employed in arbitrary quantum communication systems, including satellite-based communication systems, a particularly relevant platform for the quantum Internet.
Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here, we prove several results on efficiently learning Pauli channels and more generally the Pauli projection of a quantum channel. We first derive a procedure for learning a Pauli channel on n qubits with high probability to a relative precision ϵ using O (ϵ -2 n2 n ) measurements, which is efficient in the Hilbert space dimension. The estimate is robust to state preparation and measurement errors, which, together with the relative precision, makes it especially appropriate for applications involving characterization of high-accuracy quantum gates. Next, we show that the error rates for an arbitrary set of s Pauli errors can be estimated to a relative precision ϵ using O (ϵ -4 log s log s/ϵ) measurements. Finally, we show that when the Pauli channel is given by a Markov field with at most k -local correlations, we can learn an entire n -qubit Pauli channel to relative precision ϵ with only O k (ϵ -2 n 2 log n ) measurements, which is efficient in the number of qubits. These results enable a host of applications beyond just characterizing noise in a large-scale quantum system: they pave the way to tailoring quantum codes, optimizing decoders, and customizing fault tolerance procedures to suit a particular device.
Quantum Fisher Information is considered in Quantum Information literature as the main resource to determine a bound in the parametric characterization problem of a quantum channel by means of probe states. The parameters characterizing a quantum channel can be estimated until a limited precision settled by the Cramér–Rao bound established in estimation theory and statistics. The involved Quantum Fisher Information of the emerging quantum state provides such a bound. Quantum states with dimension d=2, the qubits, still comprise the main resources considered in Quantum Information and Quantum Processing theories. For them, Pauli channels are an important family of parametric quantum channels providing the most faithful deformation effects of imperfect quantum communication channels. Recently, Pauli channels have been characterized when they are arranged in an Indefinite Causal Order. Thus, their fidelity has been compared with single or sequential arrangements of identical channels to analyse their induced transparency under a joint behaviour. The most recent characterization has exhibited important features for quantum communication related with their parametric nature. In this work, a parallel analysis has been conducted to extended such a characterization, this time in terms of their emerging Quantum Fisher Information to pursue the advantages of each kind of arrangement for the parameter estimation problem. The objective is to reach the arrangement stating the best estimation bound for each type of Pauli channel. A complete map for such an effectivity is provided for each Pauli channel under the most affordable setups considering sequential and Indefinite Causal Order arrangements, as well as discussing their advantages and disadvantages.