Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.09358

Compressing Quantum Fisher Information

Rui Jie Tang, Jeremy Guenza Marcus, Noah Lupu-Gladstein, Arthur O. T. Pang, C. Pria Dobney, Giulio Chiribella, Aephraim M. Steinberg, Y. Batuhan Yilmaz

quant-phSubmitted Feb 10, 2026• Announced Feb 11, 2026• 0 citations
arXivHTMLPDF

Abstract

We show that the quantum Fisher information about any phase parameter encoded in a family of pure quantum states can be faithfully compressed into a single qubit, accompanied by a logarithmic amount of classical bits. When the phase is encoded into many identical copies of a qubit state on the equator of the Bloch sphere, we show that the compression can be implemented sequentially, by iteratively compressing pairs of qubits into a single qubit. We experimentally demonstrate this building block in a photonic setup, developing two alternative compression strategies, based on Type-I fusion gate and a postselected implementation of the CNOT gate.

Related papers

Compression for Quantum Population Coding

Yuxiang Yang, Ge Bai, Giulio Chiribella +1 more

We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f/2)\log n, including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f/2)\log n is the minimum amount of memory needed to achieve asymptotic faithfulness. In addition, we analyze how much of the memory needs to be quantum. We find that the ratio between quantum and classical bits can be made arbitrarily small, but cannot reach zero: unless all the quantum states in the family commute, no protocol using only classical bits can be faithful, even if it uses an arbitrarily large number of classical bits.

arXiv:1701.03372•IEEE Transactions on Information Theory•Jan 10, 2018•14 citations

Quantum Data Compression of a Qubit Ensemble

Lee A. Rozema, Dylan H. Mahler, Alex Hayat +2 more

Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even today's limited quantum memories far more powerful than previously recognized.

arXiv:1410.3941•Physical Review Letters•Oct 17, 2014•58 citations

On the role of entanglement in qudit-based circuit compression

Xiaoqin Gao, Paul Appel, Nicolai Friis +2 more

Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the major experimental challenges since it requires controlled interactions between individual systems. To make the most of quantum hardware it is crucial to process information in the most efficient way. One promising avenue is to use higher-dimensional systems, qudits, as the fundamental units of quantum information, in order to replace a fraction of the qubit-entangling gates with qudit-local gates. Here, we show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings, which we quantify by considering exemplary circuits with exactly known (multi-qubit) gate complexity. We discuss general principles for circuit compression, derive upper and lower bounds on the achievable advantage, and highlight the key role played by entanglement and the available gate set. Explicit experimental schemes for photonic as well as for trapped-ion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.

arXiv:2209.14584•Quantum•Oct 16, 2023•15 citations

Efficient compression of quantum information

Martin Plesch, Vladimír Bužek

We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform $N$ identically prepared qubits into a state, which is nontrivial only on the first $\ensuremath{\lceil}\mathrm{log}{}_{2}(N+1)\ensuremath{\rceil}$ qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-effective method for such an encoding.

arXiv:0907.1764•Physical Review A•Mar 18, 2010•49 citations

Experimental demonstration of quantum data compression

Lee A. Rozema, Dylan H. Mahler, Alex Hayat +2 more

We present experimental results implementing the Quantum Schur-Weyl Transform QSWT for three qubits, allowing us to compress three quantum bits into two. In our implementation the three qubits are encoded in two photons. The first photon encodes a path and a polarization qubit, while the second photon encodes a single polarization qubit. We use the QSWT to map all of the information from the 3 qubits onto the path and polarization qubits encoded in the first photon, allowing us to discard the second photon. We characterize our compression by performing measurements on the remaining two qubits and show that they obey the statistics of a three qubit system. We expect our technique to become extremely useful in the near future, for all quantum information architectures, as few qubit quantum memories become available.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Unbounded and lossless compression of multiparameter quantum information

Joe H. Jenne, David R. M. Arvidsson-Shukur

Several tasks in quantum-information processing involve quantum learning. For example, quantum sensing, quantum machine learning, and quantum-computer calibration involve learning and estimating unknown parameters $\mathbit{\ensuremath{\theta}}=({\ensuremath{\theta}}_{1},\ensuremath{\cdots},{\ensuremath{\theta}}_{M})$ from measurements of many copies of a quantum state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}$. This type of metrological information is described by the quantum Fisher information matrix, which bounds the average amount of information learned about $\mathbit{\ensuremath{\theta}}$ per measurement of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}$. In several scenarios, it is advantageous to compress the multiparameter information encoded in ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\bigotimes}n}$ into ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}^{\text{ps}}\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\bigotimes}m}$, where $m\ensuremath{\ll}n$. Here, we present a ``go-go'' theorem proving that $m/n$ can be made arbitrarily small, and that the information compression can happen without loss of information. We also demonstrate how to construct filters that perform this unbounded and lossless information compression. These filters can, for example, reduce arbitrarily the quantum-state intensity on experimental detectors, while retaining all initial information. Finally, we prove that the ability to compress quantum Fisher information is a nonclassical advantage that stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution.

Physical Review A•Oct 4, 2022•18 citations
We show that the quantum Fisher information about any phase parameter encoded in a family of pure quantum states can be faithfully compressed into a single qubit, accompanied by a logarithmic amount of classical bits. When the phase is encoded into many identical copies of a qubit state on the equator of the Bloch sphere, we show that the compression can be implemented sequentially, by iteratively compressing pairs of qubits into a single qubit. We experimentally demonstrate this building block in a photonic setup, developing two alternative compression strategies, based on Type-I fusion gate and a postselected implementation of the CNOT gate.
We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f/2)\log n, including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f/2)\log n is the minimum amount of memory needed to achieve asymptotic faithfulness. In addition, we analyze how much of the memory needs to be quantum. We find that the ratio between quantum and classical bits can be made arbitrarily small, but cannot reach zero: unless all the quantum states in the family commute, no protocol using only classical bits can be faithful, even if it uses an arbitrarily large number of classical bits.
Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even today's limited quantum memories far more powerful than previously recognized.
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the major experimental challenges since it requires controlled interactions between individual systems. To make the most of quantum hardware it is crucial to process information in the most efficient way. One promising avenue is to use higher-dimensional systems, qudits, as the fundamental units of quantum information, in order to replace a fraction of the qubit-entangling gates with qudit-local gates. Here, we show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings, which we quantify by considering exemplary circuits with exactly known (multi-qubit) gate complexity. We discuss general principles for circuit compression, derive upper and lower bounds on the achievable advantage, and highlight the key role played by entanglement and the available gate set. Explicit experimental schemes for photonic as well as for trapped-ion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.
We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform NNN identically prepared qubits into a state, which is nontrivial only on the first $\ensuremath{\lceil}\mathrm{log}{}_{2}(N+1)\ensuremath{\rceil}$ qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-effective method for such an encoding.
We present experimental results implementing the Quantum Schur-Weyl Transform QSWT for three qubits, allowing us to compress three quantum bits into two. In our implementation the three qubits are encoded in two photons. The first photon encodes a path and a polarization qubit, while the second photon encodes a single polarization qubit. We use the QSWT to map all of the information from the 3 qubits onto the path and polarization qubits encoded in the first photon, allowing us to discard the second photon. We characterize our compression by performing measurements on the remaining two qubits and show that they obey the statistics of a three qubit system. We expect our technique to become extremely useful in the near future, for all quantum information architectures, as few qubit quantum memories become available.
Several tasks in quantum-information processing involve quantum learning. For example, quantum sensing, quantum machine learning, and quantum-computer calibration involve learning and estimating unknown parameters $\mathbit{\ensuremath{\theta}}=({\ensuremath{\theta}}_{1},\ensuremath{\cdots},{\ensuremath{\theta}}_{M})$ from measurements of many copies of a quantum state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}$. This type of metrological information is described by the quantum Fisher information matrix, which bounds the average amount of information learned about $\mathbit{\ensuremath{\theta}}$ per measurement of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}$. In several scenarios, it is advantageous to compress the multiparameter information encoded in ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\bigotimes}n}$ into ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathbit{\ensuremath{\theta}}}^{\text{ps}}\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\bigotimes}m}$, where $m\ensuremath{\ll}n$. Here, we present a ``go-go'' theorem proving that m/nm/nm/n can be made arbitrarily small, and that the information compression can happen without loss of information. We also demonstrate how to construct filters that perform this unbounded and lossless information compression. These filters can, for example, reduce arbitrarily the quantum-state intensity on experimental detectors, while retaining all initial information. Finally, we prove that the ability to compress quantum Fisher information is a nonclassical advantage that stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution.