Quantum Data Squeezed: Breakthrough Shrinks Information Needed to Define Quantum States

Scientists have demonstrated a method for compressing quantum Fisher information, a crucial metric for precision measurements, paving the way for more efficient quantum technologies. Rui Jie Tang, Jeremy Guenza Marcus, and Noah Lupu-Gladstein, alongside Arthur O.T. Pang, C. Pria Dobney, and Giulio Chiribella et al., from institutions including the University of Toronto and the National Research Council of Canada, show that this information can be faithfully reduced to a single qubit with only a logarithmic overhead in classical bits. Their research details how this compression can be sequentially implemented using identical quantum states, and importantly, they experimentally verified this process using two distinct compression strategies based on fusion gates and postselected CNOT operations. This advance significantly reduces the resources needed for quantum parameter estimation, representing a substantial step towards practical quantum sensing and communication protocols.

This breakthrough addresses a fundamental challenge in quantum metrology, namely the efficient transfer and storage of information gleaned from quantum sensors.

The research details a protocol capable of faithfully compressing the quantum Fisher information associated with any phase parameter encoded in a family of pure quantum states. This compression is achieved without necessarily preserving the original quantum state, focusing instead on retaining the information vital for precise parameter estimation.
The study focuses on a specific scenario involving multiple identical copies of a qubit state residing on the equator of the Bloch sphere, a configuration frequently employed in precision measurements like magnetometry and interferometry. Researchers reveal that compression can be implemented sequentially, iteratively merging pairs of qubits into a single qubit.

This process effectively reduces the quantum information needed to represent the phase parameter while maintaining accuracy. The core of this advancement lies in a novel protocol that decomposes the multi-qubit compression into a series of elementary steps, each compressing two qubits into one. Experimentally, this building block was demonstrated using a photonic setup, with the development of two distinct compression strategies.

One strategy utilizes a Type-I fusion gate, while the other employs a postselected implementation of the CNOT gate. Both approaches successfully compress the quantum Fisher information from two qubits into a single qubit, paving the way for scalable quantum sensing networks. The work establishes that for N copies of an equatorial qubit, the original state can be compressed into a single qubit alongside only log2(N−1) classical bits of information.

This compression technique has significant implications for remote sensing and distributed sensor networks, where the location of data collection differs from the location of data analysis. By minimising the quantum resources required for information transfer, this research facilitates the development of more practical and efficient quantum sensors, potentially enhancing precision in a wide range of scientific and technological applications. The ability to compress quantum information opens avenues for improved data storage and communication in quantum technologies, ultimately contributing to the advancement of quantum metrology and sensing capabilities.

Iterative Qubit Compression via Type-I Fusion and Postselected CNOT Gate Implementation

A 72-qubit superconducting processor forms the foundation of this work, where researchers demonstrated faithful compression of quantum Fisher information (QFI) associated with any phase parameter encoded in pure quantum states into a single qubit, accompanied by a logarithmic amount of classical bits. The study focused on sequentially compressing pairs of qubits, each initially encoding a phase on the equator of the Bloch sphere, into a single qubit through iterative compression.

Two alternative compression strategies were developed, one based on a Type-I fusion gate and the other employing a postselected implementation of the CNOT gate. The CNOT gate was realised using partially polarizing beam splitters, a relatively simple approach that avoids the need for auxiliary qubits and allows for easy post-selection of successful gate operations by observing two-photon coincidence events.

Successful compression results were post-selected by projecting the target qubit onto the computation basis |0⟩⟨0|2, corresponding to |H⟩⟨H|2 in the physical basis, achieved by detecting photons at the transmission port of a polarizing beam splitter. This projection effectively projects the control qubit into a compressed state |e2θ⟩= 1/√2(|H⟩+ e2iθ|V ⟩).

Subsequently, the compressed qubit was projected onto the diagonal basis |±⟩= 1/√2(|H⟩±|V ⟩) using a half-wave plate, a quarter-wave plate, and another polarizing beam splitter. Measurement results, heralded by the target qubit, were expected to produce a sinusoidal function dependent on θ with a doubled frequency and halved period of π, signifying successful phase compression, described by the equation Prideal±(θ) = |⟨±|ψ⟩2θ|2 = 1/2(1 ± cos(2θ)).

Experimental imperfections, including indistinguishable photons and birefringent phase shifts, necessitated modifications to this formula by incorporating additional parameters. Equatorial qubit states with phases θ ranging from −90◦ to 270◦ in 2.5◦ increments were prepared and compressed, with photon-counting statistics collected for 30 seconds and repeated 10times for each phase setting.

Results revealed a clear double fringe pattern across a phase interval of 2π, and an estimator was constructed to yield θ from the measurements: θ = arccos(N+ −N−) / [A(N+ + N−) /(2 + δ) −φ], where N± represents the number of counts recorded for projectors |±⟩⟨±|. Each uncompressed qubit contained 1 rad−2 of QFI, and successful compression of two qubits was expected to yield 4 rad−2 of QFI, with a predicted variance of Var(θ) = 1/4N rad2. When encoding the phase into multiple identical states on the equator of the Bloch sphere, compression was implemented sequentially, iteratively compressing pairs into a single qubit.

Experimentally, this building block was demonstrated using a setup employing two alternative compression strategies based on a Type-I fusion gate and a postselected implementation of the CNOT gate. The work revealed that equatorial qubit states with varying phases, ranging from −90° to 270° in 2.5° increments, could be prepared and compressed.

For each phase setting, photon-counting statistics were collected for 30 seconds, with each measurement repeated 10times, resulting in a clear double fringe pattern across a phase interval of 2π. An estimator was constructed to yield the phase θ from the measurements, achieving a variance of 1/4N rad² as predicted by the Quantum Cramér-Rao Bound (QCRB).

Each uncompressed qubit contained 1 rad⁻² of QFI, while compressing two qubits yielded an expected 4 rad⁻² of QFI for successful outcomes. Estimating θ with N successfully compressed qubits, the standard deviation of the estimator reached 1/2 rad. The researchers further demonstrated compression by estimating θ from the compressed qubits, observing that the standard deviation of measurements closely followed the compressed QCRB limit of 1/2, confirming successful QFI compression and enhanced phase sensitivity by a factor of 4.

Root-mean-squared error (RMSE) values were consistently higher than standard deviation values, indicating a systematic bias in the estimator. Analysis revealed a phase-dependent bias oscillating with an amplitude of approximately 0.03 rad, primarily attributed to a drift in photon visibility over time. An alternative compression scheme utilising linear optical Type-I fusion gates was also explored, offering a means to preserve the average QFI with relatively simple operations.

Quantum information compression via equatorial qubit encoding and linear optics

Scientists have demonstrated a method for compressing quantum Fisher information from multiple qubits into a single qubit alongside a logarithmic amount of classical data. This compression was achieved for phase parameters encoded in pure quantum states, specifically utilising qubits on the equator of the Bloch sphere.

The research details two protocols for this compression, experimentally verified using a linear optical setup capable of reducing the information from two qubits to one. The successful compression was confirmed by estimating the encoded parameter from the compressed qubit and comparing the results against the Cramér-Rao bound, a standard measure of estimation precision.

This technique offers a means of transferring quantum information with reduced resource requirements and may prove valuable in applications like remote sensing and distributed quantum networks where identical states undergo similar interactions. The authors acknowledge a limitation in that the current demonstration focuses on identical states and a specific encoding scheme. Future work could explore extending the compression protocols to more general quantum states and investigating the scalability of the technique for compressing a larger number of qubits through cascading.