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:1811.00235

Typical Purification Reproducing the Time Evolution of an Open Quantum System

Inoue, Koki, Yoshiyuki Fukumoto

Published Nov 1, 2018• 1 citation
arXivHTMLPDF

Abstract

It is known that an arbitrary quantum state can always be expressed in a pure state by preparing an appropriate ancilla system, which is called purification. The purification can always be performed when considering only a quantity not dependent on the quantum state of the ancilla system. Otherwise, the possibility of purification cannot be elucidated. In this study, we focus on the cases where a quantum system S and the ancilla system interact with each other, and investigate whether purification, which correctly reproduces the time evolution of the system S, is possible. Accordingly, when the ancilla system is a macrosystem, it can be shown that this purification is possible for a specific initial state.

DOI
10.48550/arxiv.1811.00235

Related papers

Quantum resources for purification and cooling: fundamental limits and opportunities

Francesco Ticozzi, Lorenza Viola

Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a "virtual subsystem" which has the same dimension and is in a state with the desired purity. Beside providing a unified understanding of quantum purification dynamics in terms of a "generalized swap process," our results shed light on the significance of a no-go theorem for exact ground-state cooling, as well as on the quantum resources needed for achieving an intended purification task.

arXiv:1403.8143•Scientific Reports•Jun 5, 2014•49 citations

Resonant purification of mixed states for closed and open quantum systems

Raffaele Romano

Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system $S$ have been developed in the past years. In this work we describe a mechanism leading to purification of mixed states, based on the interaction of $S$ with an auxiliary system $P$. Considering two-level systems and assuming a particular interaction between them, we study how the dynamical parameters of the system $P$ affect the purification of $S$. By using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.

arXiv:quant-ph/0609141•Physical Review A•Feb 20, 2007•9 citations

Inhibition of Purification Processes through Zeno effect

Benedetto Militello, Anna Napoli

It is shown that a generalized quantum Zeno effect based on the introduction of a coherent coupling between several parts of a compound system can be responsible for neutralizing the effects of repeated measurements. To demonstrate this effect, we focus on a purification scheme based on iterated observations on an ancilla system put in interaction with the main one [Nakazato, Takazawa, Yuasa, Phys. Rev. Lett. {\bf 90}, 060401 (2003)]. We bring to light that a suitable Hilbert space partitioning due to an appropriate interaction can eliminate the effects of repeated wave function collapses the purification scheme is based on.

arXiv:1706.09676•Jun 29, 2017•0 citations

Peculiarities of qubit initial-state preparation by nonselective measurements on an overcomplete basis

V. V. Ignatyuk

We consider the qubit initial-state preparation due to the nonselective measurements on an overcomplete basis, when the number of outcomes $N=3$. To be specific, we have chosen the dephasing model and applied the conditions for a post-measurement state to ensure a gradual coherence enhancement at the initial stage of the system evolution. It is shown that contrary to the von Neumann--L\"uders projection scheme with $N=2$, the most mixed post-measurement state of the qubit in the general case can depend on the bath temperature. This remarkable feature allows one to consider a ``temperature-controlled'' initial purification of the open quantum system. We also consider some kinds of the repeated nonselective measurements from the viewpoint of an eventual system purification and analyze the important peculiarities of such schemes.

arXiv:1511.05206•Physical Review A•Dec 9, 2015•4 citations

Purification through Zeno-Like Measurements

Hiromichi Nakazato, Tomoko Takazawa, Kazuya Yuasa

A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the "purification" of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.

arXiv:quant-ph/0301026•Physical Review Letters•Feb 10, 2003•106 citations

Purification in rapid-repeated-interaction systems

Daniel Grimmer, Robert B. Mann, Eduardo Martín-Martínez

We investigate the open dynamics of a quantum system which is rapidly repeatedly updated by a quantum channel. Specifically, we analyze when this dynamics can purify the system. We develop a necessary and sufficient condition for such purification effects to occur and characterize their strength. We thoroughly analyze the specific scenario of a quantum system undergoing rapid unitary interactions with a sequence of ancillary quantum systems. We find that, while the purification effects are generally present, in order for these effects to be strong compared to the decoherence effects the interaction Hamiltonian must have a minimum degree of complexity. Specifically, a tensor product interaction ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Q}}_{\text{S}}\ensuremath{\bigotimes}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\text{A}}$ as well as many common light-matter interactions cannot purify efficiently.

arXiv:1611.07530•Physical Review A•Apr 10, 2017•8 citations
It is known that an arbitrary quantum state can always be expressed in a pure state by preparing an appropriate ancilla system, which is called purification. The purification can always be performed when considering only a quantity not dependent on the quantum state of the ancilla system. Otherwise, the possibility of purification cannot be elucidated. In this study, we focus on the cases where a quantum system S and the ancilla system interact with each other, and investigate whether purification, which correctly reproduces the time evolution of the system S, is possible. Accordingly, when the ancilla system is a macrosystem, it can be shown that this purification is possible for a specific initial state.
Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a "virtual subsystem" which has the same dimension and is in a state with the desired purity. Beside providing a unified understanding of quantum purification dynamics in terms of a "generalized swap process," our results shed light on the significance of a no-go theorem for exact ground-state cooling, as well as on the quantum resources needed for achieving an intended purification task.
Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system SSS have been developed in the past years. In this work we describe a mechanism leading to purification of mixed states, based on the interaction of SSS with an auxiliary system PPP. Considering two-level systems and assuming a particular interaction between them, we study how the dynamical parameters of the system PPP affect the purification of SSS. By using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.
It is shown that a generalized quantum Zeno effect based on the introduction of a coherent coupling between several parts of a compound system can be responsible for neutralizing the effects of repeated measurements. To demonstrate this effect, we focus on a purification scheme based on iterated observations on an ancilla system put in interaction with the main one [Nakazato, Takazawa, Yuasa, Phys. Rev. Lett. {\bf 90}, 060401 (2003)]. We bring to light that a suitable Hilbert space partitioning due to an appropriate interaction can eliminate the effects of repeated wave function collapses the purification scheme is based on.
We consider the qubit initial-state preparation due to the nonselective measurements on an overcomplete basis, when the number of outcomes N=3N=3N=3. To be specific, we have chosen the dephasing model and applied the conditions for a post-measurement state to ensure a gradual coherence enhancement at the initial stage of the system evolution. It is shown that contrary to the von Neumann--L\"uders projection scheme with N=2N=2N=2, the most mixed post-measurement state of the qubit in the general case can depend on the bath temperature. This remarkable feature allows one to consider a ``temperature-controlled'' initial purification of the open quantum system. We also consider some kinds of the repeated nonselective measurements from the viewpoint of an eventual system purification and analyze the important peculiarities of such schemes.
We investigate the open dynamics of a quantum system which is rapidly repeatedly updated by a quantum channel. Specifically, we analyze when this dynamics can purify the system. We develop a necessary and sufficient condition for such purification effects to occur and characterize their strength. We thoroughly analyze the specific scenario of a quantum system undergoing rapid unitary interactions with a sequence of ancillary quantum systems. We find that, while the purification effects are generally present, in order for these effects to be strong compared to the decoherence effects the interaction Hamiltonian must have a minimum degree of complexity. Specifically, a tensor product interaction ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Q}}_{\text{S}}\ensuremath{\bigotimes}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\text{A}}$ as well as many common light-matter interactions cannot purify efficiently.