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:2209.06519 · IEEE International Symposium on Information Theory (ISIT)

Compression for Qubit Clocks

Yuxiang Yang, Giulio Chiribella, Masahito Hayashi

Published Jun 1, 2018• 0 citations
arXivHTMLPDF

Abstract

Two-Ievel (qubit) clock systems are often used to perform precise measurement of time. In this work, we propose a compression protocol for n identically prepared states of qubit clocks. The protocol faithfully encodes the states into (1/2) logn qubits and (1/2) logn classical bits and works even in the presence of noise. If the purity of the clock states is fixed, (1/2) logn qubits are sufficient. We also prove that this protocol requires the minimum amount of total memory among all protocols with vanishing error in the large n limit.

DOI
10.1109/isit.2018.8437783

Related papers

Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States

Yuxiang Yang, Giulio Chiribella, Daniel Ebler

We present one-shot compression protocols that optimally encode ensembles of N identically prepared mixed states into O(logN) qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.

arXiv:1506.03542•Physical Review Letters•Feb 23, 2016•28 citations

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

Compression for quantum population coding

Yuxiang Yang, Ge Bai, Giulio Chiribella +1 more

We study the compression of arbitrary parametric families of n identically prepared finite-dimensional quantum states, in a setting that can be regarded as a quantum analogue of population coding. For a family with f free parameters, we propose an asymptotically faithful protocol that requires a memory of overall size (f/2) log n. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of the optimal compression of n identically prepared displaced thermal states. Our protocol achieves the ultimate bound predicted by quantum Shannon theory. In addition, we explore the minimum requirement for quantum memory: On the one hand, the amount of quantum memory used by our protocol can be made arbitrarily small compared to the overall memory cost; on the other hand, any protocol using only classical memory cannot be faithful.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2017•4 citations

Quantum Stopwatch: How To Efficiently Store Time in a Quantum Memory

Yuxiang Yang, Giulio Chiribella, Masahito Hayashi

Atomic clocks are our most accurate indicators of time. Their applications range from GPS systems to synchronization of electronics, astronomical observations, and tests of fundamental physics. Here we propose a protocol that combines an atomic clock with a quantum memory, realizing a stopwatch that can be paused and resumed on demand. Taking advantage of the quantum memory, the stopwatch can measure the total time elapsed in a sequence of time intervals with the ultimate precision allowed by quantum mechanics, outperforming stopwatches that use only classical memories. The working principle of the quantum stopwatch is a new type of information compression,tailored to store the state of the quantum clock into a quantum memory of exponentially smaller size. Our protocol can be used to generate quantum states with Heisenberg limited sensitivity and to efficiently synchronize clocks in quantum communication networks.

•Mar 17, 2017•0 citations

Compressing Quantum Fisher Information

Rui Jie Tang, Jeremy Guenza Marcus, Noah Lupu-Gladstein +5 more

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.

quant-pharXiv:2602.09358•Feb 11, 2026•0 citations

Optimal Compression for Ensembles of Identically Prepared Mixed States

Yuxiang Yang, Daniel Ebler, Giulio Chiribella

We present an universal protocol, capable of compressing $N$ copies of a completely unknown mixed state into $O(\log N)$ qubits in a lossless fashion. Our result demonstrates that the exponential compression of identically prepared pure states, recently implemented in a prototype experiment by Rozema et. al. [Phys. Rev. Lett. 113, 160504 (2014)], can be extended to arbitrary mixed states, despite the fact that the latter cover an exponentially large space. Furthermore, we highlight a striking difference between the pure and the mixed state case, showing that, if the spectrum is known with sufficient precision, the number of qubits needed for compression of a mixed state will drop down discontinuously as soon as a small recovery error is allowed.

•Jun 11, 2015•1 citation
Two-Ievel (qubit) clock systems are often used to perform precise measurement of time. In this work, we propose a compression protocol for n identically prepared states of qubit clocks. The protocol faithfully encodes the states into (1/2) logn qubits and (1/2) logn classical bits and works even in the presence of noise. If the purity of the clock states is fixed, (1/2) logn qubits are sufficient. We also prove that this protocol requires the minimum amount of total memory among all protocols with vanishing error in the large n limit.
We present one-shot compression protocols that optimally encode ensembles of N identically prepared mixed states into O(logN) qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.
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.
We study the compression of arbitrary parametric families of n identically prepared finite-dimensional quantum states, in a setting that can be regarded as a quantum analogue of population coding. For a family with f free parameters, we propose an asymptotically faithful protocol that requires a memory of overall size (f/2) log n. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of the optimal compression of n identically prepared displaced thermal states. Our protocol achieves the ultimate bound predicted by quantum Shannon theory. In addition, we explore the minimum requirement for quantum memory: On the one hand, the amount of quantum memory used by our protocol can be made arbitrarily small compared to the overall memory cost; on the other hand, any protocol using only classical memory cannot be faithful.
Atomic clocks are our most accurate indicators of time. Their applications range from GPS systems to synchronization of electronics, astronomical observations, and tests of fundamental physics. Here we propose a protocol that combines an atomic clock with a quantum memory, realizing a stopwatch that can be paused and resumed on demand. Taking advantage of the quantum memory, the stopwatch can measure the total time elapsed in a sequence of time intervals with the ultimate precision allowed by quantum mechanics, outperforming stopwatches that use only classical memories. The working principle of the quantum stopwatch is a new type of information compression,tailored to store the state of the quantum clock into a quantum memory of exponentially smaller size. Our protocol can be used to generate quantum states with Heisenberg limited sensitivity and to efficiently synchronize clocks in quantum communication networks.
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 present an universal protocol, capable of compressing NNN copies of a completely unknown mixed state into O(log⁡N)O(\log N)O(logN) qubits in a lossless fashion. Our result demonstrates that the exponential compression of identically prepared pure states, recently implemented in a prototype experiment by Rozema et. al. [Phys. Rev. Lett. 113, 160504 (2014)], can be extended to arbitrary mixed states, despite the fact that the latter cover an exponentially large space. Furthermore, we highlight a striking difference between the pure and the mixed state case, showing that, if the spectrum is known with sufficient precision, the number of qubits needed for compression of a mixed state will drop down discontinuously as soon as a small recovery error is allowed.