Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

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Non-Hermitian fractional quantum Hall states

Scientific Reports ◽

10.1038/s41598-019-53253-8 ◽

2019 ◽

Vol 9 (1) ◽

Cited By ~ 26

Author(s):

Tsuneya Yoshida ◽

Koji Kudo ◽

Yasuhiro Hatsugai

Keyword(s):

Ground State ◽

Cold Atoms ◽

Quantum Hall ◽

Quantum Zeno Effect ◽

Many Body ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Zeno Effect ◽

Quantum Hall States ◽

The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

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Ultracold quantum wires with localized losses: Many-body quantum Zeno effect

Physical Review B ◽

10.1103/physrevb.101.144301 ◽

2020 ◽

Vol 101 (14) ◽

Cited By ~ 9

Author(s):

Heinrich Fröml ◽

Christopher Muckel ◽

Corinna Kollath ◽

Alessio Chiocchetta ◽

Sebastian Diehl

Keyword(s):

Quantum Wires ◽

Quantum Zeno Effect ◽

Many Body ◽

Zeno Effect

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Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency

Quantum ◽

10.22331/q-2021-09-29-556 ◽

2021 ◽

Vol 5 ◽

pp. 556

Author(s):

Giovanni Cataldi ◽

Ashkan Abedi ◽

Giuseppe Magnifico ◽

Simone Notarnicola ◽

Nicola Dalla Pozza ◽

...

Keyword(s):

Transverse Field ◽

Matrix Product ◽

Hilbert Curve ◽

Many Body ◽

Network Efficiency ◽

Lattice Systems ◽

Tensor Network ◽

Quantum Ising Model ◽

1D Chain ◽

Numerical Precision

We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to 64×64, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.

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Quantum information processing with quantum zeno many-body dynamics

Quantum Information and Computation ◽

10.26421/qic10.3-4-3 ◽

2010 ◽

Vol 10 (3&4) ◽

pp. 201-222

Author(s):

A. Monras ◽

O. Romero-Isart

Keyword(s):

Quantum Information ◽

Quantum Information Processing ◽

Quantum Zeno Effect ◽

Quantum State Transfer ◽

Many Body ◽

One Dimensional ◽

Zeno Effect ◽

State Transfer ◽

Body Dynamics ◽

Universal Quantum

We show how the quantum Zeno effect can be exploited to control quantum many-body dynamics for quantum information and computation purposes. In particular, we consider a one dimensional array of three level systems interacting via a nearest-neighbour interaction. By encoding the qubit on two levels and using simple projective frequent measurements yielding the quantum Zeno effect, we demonstrate how to implement a well defined quantum register, quantum state transfer on demand, universal two-qubit gates and two-qubit parity measurements. Thus, we argue that the main ingredients for universal quantum computation can be achieved in a spin chain with an {\em always-on} and {\em constant} many-body Hamiltonian. We also show some possible modifications of the initially assumed dynamics in order to create maximally entangled qubit pairs and single qubit gates.

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