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arXiv:1908.10735 · IEEE Journal on Selected Areas in Communications

Channel Coding of a Quantum Measurement

Spiros Kechrimparis, Chahan M. Kropf, Filip Wudarski, Joonwoo Bae

Published Jan 24, 2020• 13 citations
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Abstract

In this work, we consider the preservation of a measurement for quantum systems interacting with an environment. Namely, a method of preserving an optimal measurement over a channel is devised, what we call channel coding of a quantum measurement in that operations are applied before and after a channel in order to protect a measurement. A protocol that preserves a quantum measurement over an arbitrary channel is shown only with local operations and classical communication without the use of a larger Hilbert space. Therefore, the protocol is readily feasible with present day's technologies. Channel coding of qubit measurements is presented, and it is shown that a measurement can be preserved for an arbitrary channel for both i) pairs of qubit states and ii) ensembles of equally probable states. The protocol of preserving a quantum measurement is demonstrated with IBM quantum computers.

DOI
10.1109/jsac.2020.2969034

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One of the consequences in the distribution of quantum states over a long distance is that, since resulting quantum states are noisy due to the intervention of an environment, a measurement setting should be re-aligned to optimize detection events, for which additional experimental resources such as quantum tomography of a channel or resulting states is necessary. In this work, we present a protocol for protecting an optimal measurement setup without verifying a channel. A receiver does not have to revise the measurement prepared in a noiseless scenario since it would remain optimal for quantum states resulting from an unknown and noisy channel. The measurement protection protocol realizes a supermap describing transformations over quantum channels and is experimentally feasible as it only applies local unitary transformations before and after the transmission. We present experimental proof-of-principle demonstrations of the measurement protection protocol. We also apply the measurement protection to a prepare-and-measure protocol, the Bennett-Brassard 1984 (BB84) protocol, and find that preserving an optimal measurement can suppress quantum-bit error rates, allowing the protocol to tolerate an even higher noise during transmission. The BB84 protocol with the measurement protection is experimentally demonstrated with the polarization encoding on photonic qubits.
Abstract We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the characterization of optimal measurement preserving (OMP) channels for a given qubit ensemble, e.g., a set of two states or a set of multiple qubit states with equal a priori probabilities. Conversely, we also characterize qubit ensembles for which a given channel is OMP, such as unitary and depolarization channels. Finally, we show how the sets of OMP channels for a given ensemble can be constructed.
All free-space quantum communications require the use of a quantum channel, which transports quantum bits in such a way that the quantum mechanical states of the qubits remain preserved from one end of the channel to the other one. In quantum computing the classical error coding methods could not be used, however we can construct a classical channel with zero redundancy error correction for any unitary channel. In our basically new quantum error correction approach, the classical states are coded into the eigenvectors and unitary transformations. In this paper, we show that with our new algorithm it’s possible to create redundancy-free quantum error correction. We also consider the redundancy-free implementation of a unitary error correcting operator. Our protocol achieves the redundancy-free quantum communication using local unitary operations and unitary matrices. These solutions could be useful for the free-space quantum communication.
Transmitting information about quantum states over classical noisy channels is an important problem with applications to science, computing, and sensing. This task, however, poses fundamental challenges due to the exponential scaling of state space with system size. We introduce shadow tomography-based transmission with unequal error protection (STT-UEP), a novel communication protocol that enables efficient transmission of properties of quantum states, allowing decoder-side estimation of arbitrary local Pauli observables. Unlike conventional approaches requiring the transmission of a number of bits that is exponential in the number of qubits, STT-UEP achieves communication complexity that scales logarithmically with the number of observables, depending on the observable weight. The protocol exploits classical shadow tomography for measurement efficiency, and applies unequal error protection by encoding measurement bases with stronger channel codes than measurement outcomes. We provide theoretical guarantees on estimation accuracy as a function of the bit error probability of the classical channel, and validate the approach against several benchmarks via numerical results.