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:1706.05600 · Physical Review A

Entanglement increase from local interaction in the absence of initial quantum correlation in the environment and between the system and the environment

Iman Sargolzahi, Sayyed Yahya Mirafzali

Published Feb 23, 2018• 5 citations
arXivHTMLPDF

Abstract

We consider a bipartite quantum system $S=AB$ such that the part $A$ is isolated from the environment $E$ and only the part $B$ interacts with $E$. Under such circumstances, entanglement of the system may experience decreases and increases, during the evolution of the system. Here, we show that the entanglement of the system can exceed its initial value, under such local interaction, even though, at the initial moment, there is no entanglement in the environment and the system and the environment are only classically correlated. The case which is studied in this paper possesses another interesting feature too: The reduced dynamics of the system can be modeled as a completely positive map. In addition, we introduce the concept of inaccessible entanglement to explain why entanglement can exceed its initial value, under local interactions, in open quantum systems.

DOI
10.1103/physreva.97.022331

Related papers

Entanglement recovering under local non-positive reduced dynamics

Iman Sargolzahi

Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by $\mathcal{E}_{A}\otimes \mathcal{E}_{B}$, where $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as $Ψ_{A}\otimes Ψ_{B}$, where $Ψ_{A}$ and $Ψ_{B}$ are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement $\textit{ex nihilo}$.

quant-pharXiv:2605.08923•Brazilian Journal of Physics•May 12, 2026•0 citations

Initial Correlations and Complete Positivity of Dynamical Maps

Vinayak Jagadish, R. Srikanth, Francesco Petruccione

It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

Open Systems & Information Dynamics•Sep 1, 2023•2 citations

Dynamics of initially correlated open quantum systems: Theory and applications

Gerardo A. Paz-Silva, Michael J. W. Hall, Howard M. Wiseman

We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of ${d}^{2}$ (or less) completely positive maps, where $d$ is the dimension of the system. Only one such map is required for the special case of no initial correlations. The same maps describe the dynamics of any system-environment state obtained from the initial state by a local operation on the system. The reduction of the system dynamics to a set of completely positive maps allows known numerical and analytic tools for uncorrelated initial states to be applied to the general case of initially correlated states, which we exemplify by solving the qubit dephasing model for such states, and provides a natural approach to quantum Markovianity for this case. We show that this set of completely positive maps can be experimentally characterized using only local operations on the system, via a generalization of noise spectroscopy protocols. As further applications, we first consider the problem of retrodicting the dynamics of an open quantum system which is in an arbitrary state when it becomes accessible to the experimenter and explore the conditions under which retrodiction is possible. We also introduce a related one-sided or limited-access tomography protocol for determining an arbitrary bipartite state, evolving under a sufficiently rich Hamiltonian, via local operations and measurements on just one component. We simulate this protocol for a physical model of particular relevance to nitrogen-vacancy centers and in particular show how to reconstruct the density matrix of a set of three qubits, interacting via dipolar coupling and in the presence of local magnetic fields, by measuring and controlling only one of them.

arXiv:1810.12540•Physical Review A•Oct 25, 2019•33 citations

Initial correlations in open quantum systems are always detectable

Iman Sargolzahi

Consider an open quantum system which interacts with its environment. Assuming that the experimenter has access only to the system, an interesting question is whether it is possible to detect initial correlations between the system and the environment by performing measurements only on the system. Various methods have been proposed to detect correlations by local measurements on the system. After reviewing these methods, we will show that initial correlations between the system and the environment are always detectable. In particular, we will show that one can always find a unitary evolution, for the whole system-environment, such that the trace distance method, proposed to witness correlations locally, succeeds. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. Next, we address the case where the system and the environment interact through a time-independent Hamiltonian. For this case we will see that if the initial correlation can be detected locally at some time $t$, then it can be detected for almost all the other times too. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable even though the unitary evolution, generated by the Hamiltonian, is not factorized.

arXiv:2311.03849•Physical Review A•Feb 12, 2024•1 citation

Entanglement in open quantum dynamics

Аурелиан Исар

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuousvariable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment.Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state.For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled.In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement.We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable.We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.

•Dec 3, 2012•16 citations

Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the resulting consequences

Katarzyna Roszak, Łukasz Cywiński

We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume, and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In the case of the discord with respect to the qubit, a vast majority of qubit-environment separable states is discordant, but in specific situations zero-discord states are possible. This is conceptually important since there is a connection between the discordance with respect to a given subsystem and the possibility of describing the evolution of this subsystem using completely positive maps. Finally, we use the formalism to find an exemplary evolution of an entangled state of two qubits that is completely positive, and occurs solely due to interaction of only one of the qubits with its environment (so one could guess that it corresponds to a local operation, since it is local in a physical sense), but which nevertheless causes the enhancement of entanglement between the qubits. While this simply means that the considered evolution is completely positive, but does not belong to local operations and classical communication, it shows how much caution has to be exercised when identifying evolution channels that belong to that class.

arXiv:1709.00558•Physical Review A•Jan 10, 2018•29 citations
We consider a bipartite quantum system S=ABS=ABS=AB such that the part AAA is isolated from the environment EEE and only the part BBB interacts with EEE. Under such circumstances, entanglement of the system may experience decreases and increases, during the evolution of the system. Here, we show that the entanglement of the system can exceed its initial value, under such local interaction, even though, at the initial moment, there is no entanglement in the environment and the system and the environment are only classically correlated. The case which is studied in this paper possesses another interesting feature too: The reduced dynamics of the system can be modeled as a completely positive map. In addition, we introduce the concept of inaccessible entanglement to explain why entanglement can exceed its initial value, under local interactions, in open quantum systems.
Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by EA⊗EB\mathcal{E}_{A}\otimes \mathcal{E}_{B}EA​⊗EB​, where EA\mathcal{E}_{A}EA​ and EB\mathcal{E}_{B}EB​ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as ΨA⊗ΨBΨ_{A}\otimes Ψ_{B}ΨA​⊗ΨB​, where ΨAΨ_{A}ΨA​ and ΨBΨ_{B}ΨB​ are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement ex nihilo\textit{ex nihilo}ex nihilo.
It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.
We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of d2{d}^{2}d2 (or less) completely positive maps, where ddd is the dimension of the system. Only one such map is required for the special case of no initial correlations. The same maps describe the dynamics of any system-environment state obtained from the initial state by a local operation on the system. The reduction of the system dynamics to a set of completely positive maps allows known numerical and analytic tools for uncorrelated initial states to be applied to the general case of initially correlated states, which we exemplify by solving the qubit dephasing model for such states, and provides a natural approach to quantum Markovianity for this case. We show that this set of completely positive maps can be experimentally characterized using only local operations on the system, via a generalization of noise spectroscopy protocols. As further applications, we first consider the problem of retrodicting the dynamics of an open quantum system which is in an arbitrary state when it becomes accessible to the experimenter and explore the conditions under which retrodiction is possible. We also introduce a related one-sided or limited-access tomography protocol for determining an arbitrary bipartite state, evolving under a sufficiently rich Hamiltonian, via local operations and measurements on just one component. We simulate this protocol for a physical model of particular relevance to nitrogen-vacancy centers and in particular show how to reconstruct the density matrix of a set of three qubits, interacting via dipolar coupling and in the presence of local magnetic fields, by measuring and controlling only one of them.
Consider an open quantum system which interacts with its environment. Assuming that the experimenter has access only to the system, an interesting question is whether it is possible to detect initial correlations between the system and the environment by performing measurements only on the system. Various methods have been proposed to detect correlations by local measurements on the system. After reviewing these methods, we will show that initial correlations between the system and the environment are always detectable. In particular, we will show that one can always find a unitary evolution, for the whole system-environment, such that the trace distance method, proposed to witness correlations locally, succeeds. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. Next, we address the case where the system and the environment interact through a time-independent Hamiltonian. For this case we will see that if the initial correlation can be detected locally at some time ttt, then it can be detected for almost all the other times too. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable even though the unitary evolution, generated by the Hamiltonian, is not factorized.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuousvariable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment.Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state.For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled.In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement.We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable.We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume, and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In the case of the discord with respect to the qubit, a vast majority of qubit-environment separable states is discordant, but in specific situations zero-discord states are possible. This is conceptually important since there is a connection between the discordance with respect to a given subsystem and the possibility of describing the evolution of this subsystem using completely positive maps. Finally, we use the formalism to find an exemplary evolution of an entangled state of two qubits that is completely positive, and occurs solely due to interaction of only one of the qubits with its environment (so one could guess that it corresponds to a local operation, since it is local in a physical sense), but which nevertheless causes the enhancement of entanglement between the qubits. While this simply means that the considered evolution is completely positive, but does not belong to local operations and classical communication, it shows how much caution has to be exercised when identifying evolution channels that belong to that class.