# Quantum compression of tensor network states

@article{Bai2020QuantumCO, title={Quantum compression of tensor network states}, author={Ge Bai and Yuxiang Yang and Giulio Chiribella}, journal={New Journal of Physics}, year={2020} }

We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by the minimum cut of a suitable flow network, and is related to the flow of information from the manifold of parameters that specify the states to the physical systems in which the states are embodied. For given network topology and given edge dimensions, our… Expand

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#### References

SHOWING 1-10 OF 72 REFERENCES

Attaining the Ultimate Precision Limit in Quantum State Estimation

- Physics, Mathematics
- Communications in Mathematical Physics
- 2019

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold… Expand

Many-body effects in quantum metrology

- Physics
- New Journal of Physics
- 2019

We study the impact of many-body effects on the fundamental precision limits in quantum metrology. On the one hand such effects may lead to non-linear Hamiltonians, studied in the field of non-linear… Expand

Single-Shot Holographic Compression from the Area Law.

- Medicine, Physics
- Physical review letters
- 2019

It is shown that, for any state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened boundary of the region. Expand

Compression for Quantum Population Coding

- Physics, Computer Science
- IEEE Transactions on Information Theory
- 2018

It is found 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 classicalbits can be faithful, even if it uses an arbitrarily large number of classical bits. Expand

Quantum stopwatch: how to store time in a quantum memory

- Computer Science, Medicine
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

This work introduces a method that, in principle, eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Expand

Nonlinear Quantum Metrology of Many-Body Open Systems.

- Physics, Medicine
- Physical review letters
- 2017

It is shown that one can estimate the system-environment coupling parameter with precision N^{-(p/2)}, while many-body decoherence enhances the precision to N^{-k} in the noise-amplitude estimation of a fluctuating k-body Hamiltonian. Expand

- 2016

Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States.

- Physics, Medicine
- Physical review letters
- 2016

One-shot compression protocols that optimally encode ensembles of N identically prepared mixed states into O(logN) qubits are presented, finding 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. Expand

Optimal compression for identically prepared qubit states

- Mathematics, Physics
- Physical review letters
- 2016

The ultimate limits to the compression of sequences of identically prepared qubits are established through use of the optimal universal cloning machine, which finds here a novel application to quantum Shannon theory. Expand

- Flows in Networks
- 2015