Simulation Separability — An Intrinsic Notion of Separability
(2026) FYSM34 20261Department of Physics
Mathematical Physics
- Abstract
- Entanglement is not an intrinsic property of a quantum state: it depends on how the total system is factorized into subsystems via a tensor product structure. Just as a coherent quantum state can be made to appear classical by representing it in its eigenbasis, an entangled state can always be made to appear separable in a suitably chosen factorization. However, the same is not true for a set of states. It is not always possible to make a set of states simultaneously separable in a common factorization. Following recent work that defined a basis-independent notion of classicality for sets of states, we propose an extension of this idea to sets of bipartite states. This leads us to a factorization-independent notion of separability we call... (More)
- Entanglement is not an intrinsic property of a quantum state: it depends on how the total system is factorized into subsystems via a tensor product structure. Just as a coherent quantum state can be made to appear classical by representing it in its eigenbasis, an entangled state can always be made to appear separable in a suitably chosen factorization. However, the same is not true for a set of states. It is not always possible to make a set of states simultaneously separable in a common factorization. Following recent work that defined a basis-independent notion of classicality for sets of states, we propose an extension of this idea to sets of bipartite states. This leads us to a factorization-independent notion of separability we call simulation separability.
This notion is weaker than previously studied forms of separability for sets of states. It can be physically understood via an operational interpretation based on unitary gates and state-preparation devices that emit separable states. By showing that the set of all simulation-separable sets is convex, we are able to derive necessary and sufficient conditions for simulation separability. We also propose an experimentally implementable method for detecting sets that are not simulation separable. Finally, finite sets of two-qubit states are investigated numerically with respect to simulation separability. (Less) - Popular Abstract
- Entanglement lies behind many of the advantages promised by upcoming quantum technologies. A quantum state is called entangled when it describes several parts of a system in a way that cannot be reduced to descriptions of the parts separately. If such a reduction is possible, the state is called separable. However, whether a state is entangled or separable depends on how the system is divided into parts.
In principle, this division can depend on the perspective of the observer. A single entangled state can always be made to appear separable by choosing a suitable way of dividing the system. The same need not be true for a whole collection of states: different states may require different divisions to appear separable. In this thesis, we... (More) - Entanglement lies behind many of the advantages promised by upcoming quantum technologies. A quantum state is called entangled when it describes several parts of a system in a way that cannot be reduced to descriptions of the parts separately. If such a reduction is possible, the state is called separable. However, whether a state is entangled or separable depends on how the system is divided into parts.
In principle, this division can depend on the perspective of the observer. A single entangled state can always be made to appear separable by choosing a suitable way of dividing the system. The same need not be true for a whole collection of states: different states may require different divisions to appear separable. In this thesis, we use this observation to define a perspective-independent notion of separability, called simulation separability.
Roughly speaking, a collection of states is simulation separable if it can be reproduced using devices that produce separable states. The caveat is that each device may use a different preferred division of the system, meaning that the devices may disagree on which states they regard as separable. We also develop methods for studying when such simulations are possible, and when they are not. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/student-papers/record/9242260
- author
- Lindén Åsell, Tim LU
- supervisor
- organization
- course
- FYSM34 20261
- year
- 2026
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- quantum information theory, separability, entanglement, intrinsic notion, tensor product structure, factorization algebra, simulation, operational, quantum foundations, set of states, set of density matrices, tensor products, unitarily invariant, state-preparation devices, factorization-independent, factorizations, frame independent, reference frames, classical model, separable model, classicality, quantum feature, subalgebras
- language
- English
- id
- 9242260
- date added to LUP
- 2026-07-01 20:43:29
- date last changed
- 2026-07-01 20:43:29
@misc{9242260,
abstract = {{Entanglement is not an intrinsic property of a quantum state: it depends on how the total system is factorized into subsystems via a tensor product structure. Just as a coherent quantum state can be made to appear classical by representing it in its eigenbasis, an entangled state can always be made to appear separable in a suitably chosen factorization. However, the same is not true for a set of states. It is not always possible to make a set of states simultaneously separable in a common factorization. Following recent work that defined a basis-independent notion of classicality for sets of states, we propose an extension of this idea to sets of bipartite states. This leads us to a factorization-independent notion of separability we call simulation separability.
This notion is weaker than previously studied forms of separability for sets of states. It can be physically understood via an operational interpretation based on unitary gates and state-preparation devices that emit separable states. By showing that the set of all simulation-separable sets is convex, we are able to derive necessary and sufficient conditions for simulation separability. We also propose an experimentally implementable method for detecting sets that are not simulation separable. Finally, finite sets of two-qubit states are investigated numerically with respect to simulation separability.}},
author = {{Lindén Åsell, Tim}},
language = {{eng}},
note = {{Student Paper}},
title = {{Simulation Separability — An Intrinsic Notion of Separability}},
year = {{2026}},
}