Experimental Quantum Channel Discrimination Using Metastable States of a Trapped Ion

Kyle DeBry, Jasmine Sinanan-Singh, Colin D. Bruzewicz, David Reens, May E. Kim, Matthew P. Roychowdhury, Robert McConnell, Isaac L. Chuang, and John Chiaverini

Phys. Rev. Lett. 131, 170602 – Published 25 October 2023

Abstract

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped ${}^{40}{Ca}^{+}$ ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the six-dimensional $D_{5 / 2}$ state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding 99% in each case, limited entirely by known experimental imperfections.

Received 2 June 2023
Accepted 17 August 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.170602

Physics Subject Headings (PhySH)

Quantum channels Quantum information with trapped ions Quantum protocols

Trapped ions

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Kyle DeBry ^1,2,*, Jasmine Sinanan-Singh¹, Colin D. Bruzewicz², David Reens², May E. Kim ², Matthew P. Roychowdhury², Robert McConnell², Isaac L. Chuang¹, and John Chiaverini^2,3

¹Department of Physics, Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
³Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*debry@mit.edu

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Issue

Vol. 131, Iss. 17 — 27 October 2023

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Images

Figure 1
Operations and atomic states used in the channel-discrimination protocols. (a) Bloch sphere showing PSK rotations, with colored arrows showing rotation axes at angles of 0, $2 π / 3$ , and $4 π / 3$ in the $\hat{x} - \hat{y}$ plane, relative to $\hat{x}$ . (b) Bloch sphere showing ASK rotations about $\hat{x}$ . (c) Energy level diagram of the relevant states and transitions of ${}^{40}{Ca}^{+}$ ions. (d) Quantum circuit diagram for the PSK protocol. Gates shaded red are performed using the 729 nm laser, and all others are performed with the 8.6 MHz rf drive. Precomputed processing gates $U_{i}$ are shaded blue. Gates labeled with the yellow question mark icon represent the oracle.
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Figure 2
Experimental data of the three-phase PSK algorithm as a function of evolution time. The pulse sequence representation along the top has colors and labels matching those in Fig. 1. The chart below is lightly shaded to highlight when each pulse is being applied. The phase of the oracle’s $π$ pulse is indicated on the right side of the figure. The three colors and shapes of points correspond to the probability of measuring each readout state [see Fig. 1]. Each point corresponds to 200 trials, and the experimental data are overlaid on a zero-free-parameter simulation of the expected performance of the algorithm, displayed as solid lines. Error bars represent $1 σ$ confidence intervals.
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Figure 3
Input-output plot showing the response of channel discrimination protocols as a function of the signal angle for the channel. For ASK protocols, the signal angle is the rotation angle $θ$ , and for the PSK protocol it is the phase $ϕ$ . Error bars represent $1 σ$ confidence intervals, but are smaller than data point symbols in most cases. Data points correspond to 200 trials. (a) Theory curves for an ASK protocol implemented with qubits [SU(2)]. (b) ASK protocol performed in the $D_{5 / 2}$ manifold [SU(6)], with data points overlaid on solid theory curves. (c) PSK performed in the $D_{5 / 2}$ manifold [SU(6)], with data points overlaid on solid theory curves.
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Figure 4
Populations and magnitudes of population deviations from optimal (the $3 \times 3$ identity matrix) for each possible oracle value for both phase- and amplitude-shift keying implementations of the three-channel discrimination problem. The data for each signal angle correspond to 10 000 trials. (a) PSK populations. (b) Magnitude of PSK deviation from optimal. (c) ASK populations. (d) Magnitude of ASK deviation from optimal.
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