In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We state and prove a novel sufficient condition for SBS to arise dynamically for finite-dimensional systems. The condition is based on the Gram–Schmidt orthogonalization rather than on the Knill–Barnum error estimation used in previous papers.In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We state and prove a novel sufficient condition for SBS to arise dynamically for finite-dimensional systems. The condition is based on the Gram–Schmidt orthogonalization rather than on the Knill–Barnum error estimation used in previous papers.

arXiv:2403.01419Journal of Mathematical PhysicsDec 1, 20241 citation

Decoherence and objectivity in higher spin environments

Mateusz Kiciński, Jarosław K. Korbicz

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin- $1/2$ systems only, and we hope will be useful in future objectivity experiments.We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments.

arXiv:2105.09093Physical Review AOct 21, 202110 citations

Encoding position by spins: Objectivity in the boson-spin model

Tae-Hun Lee, Jarosław K. Korbicz

We investigate quantum objectivity in the boson-spin model, where a central harmonic oscillator interacts with a thermal bath of spin- $\frac{1}{2}$ systems. We analyze how information about a continuous position variable can be encoded into discrete, finite-dimensional environments. More precisely, we study conditions under which the so-called spectrum broadcast structures can be formed in the model. These are multipartite quantum-state structures, representing a mode-refined form of decoherence. Working in the recoil-less limit, we use the Floquet theory to show that despite its apparent simplicity, the model has a rich structure with different regimes, depending on the motion of the central system. In one of them, the faithful encoding of the position and hence objectivity are impossible irrespectively of the resources used. In another, large enough collections of spins will faithfully encode the position information. We derive the characteristic length scales, corresponding to decoherence and precision of the encoding.We investigate quantum objectivity in the boson-spin model, where a central harmonic oscillator interacts with a thermal bath of spin-$\frac{1}{2}$ systems. We analyze how information about a continuous position variable can be encoded into discrete, finite-dimensional environments. More precisely, we study conditions under which the so-called spectrum broadcast structures can be formed in the model. These are multipartite quantum-state structures, representing a mode-refined form of decoherence. Working in the recoil-less limit, we use the Floquet theory to show that despite its apparent simplicity, the model has a rich structure with different regimes, depending on the motion of the central system. In one of them, the faithful encoding of the position and hence objectivity are impossible irrespectively of the resources used. In another, large enough collections of spins will faithfully encode the position information. We derive the characteristic length scales, corresponding to decoherence and precision of the encoding.

arXiv:2401.07690Physical Review AMay 3, 20244 citations

Glimpse of objectivity in bipartite systems for nonentangling pure dephasing evolutions

Katarzyna Roszak, Jarosław K. Korbicz

We study separable system-environment evolutions of pure dephasing type in the context of objectivity. We find that it can lead to the natural emergence of spectrum broadcast structures (SBSs), but at discrete time instances. Contrary to the standard way of obtaining SBS states, which requires entanglement, reaching such states here does not require decoherence (no unobserved environments are necessary). Yet the biggest difference is the basis with respect to which the SBS states are formed. Here it is not the pointer basis of the system given by the interaction with the environment, but their equal superposition basis, the so-called mutually unbiased basis. The price to pay is a simple SBS structure with just one environment and its momentary character.We study separable system-environment evolutions of pure dephasing type in the context of objectivity. We find that it can lead to the natural emergence of spectrum broadcast structures (SBSs), but at discrete time instances. Contrary to the standard way of obtaining SBS states, which requires entanglement, reaching such states here does not require decoherence (no unobserved environments are necessary). Yet the biggest difference is the basis with respect to which the SBS states are formed. Here it is not the pointer basis of the system given by the interaction with the environment, but their equal superposition basis, the so-called mutually unbiased basis. The price to pay is a simple SBS structure with just one environment and its momentary character.

arXiv:1911.05558Physical Review AMay 27, 20208 citations

Analytical studies of spectrum broadcast structures in quantum Brownian motion

Jan Tuziemski, Jarosław K. Korbicz

Abstract Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.Abstract Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.

arXiv:1603.04217Journal of Physics A Mathematical and TheoreticalOct 5, 201613 citations

Quantum Darwinism and objectivity in non-trivial systems and interactions

Eoghan Ryan

An explanation for the quantum-to-classical transition has long been sought after since the haydays of the field. Decoherence theory and open quantum system dynamics have paved the way, showing how a system can become correlated with, and so lose information into the environment. Quantum Darwinism, and its more stringent cousins Strong Quantum Darwinism and Spectrum Broadcast Structures, seek to explain how this information loss is achieved in such a way as to be objective, classical and redundant. However there remains questions as to how the structure of the environment, states and types of interactions can give rise to this redundant encoding. In this thesis, we collect the work of 3 of our papers, exploring these questions. First, we show how information from one environment can spread to another. Then we show how commutativity can play a role in the emergence of objectivity. Lastly, we move beyond a single, pure system to a more realistic bipartite one, with both classical and quantum correlations between the subsystems. We shall show how interactions between only these subsystems can mediate the redundancy of others, and how these can lower bound and upper bound other forms of interactions between said subsystems and the environment.An explanation for the quantum-to-classical transition has long been sought after since the haydays of the field. Decoherence theory and open quantum system dynamics have paved the way, showing how a system can become correlated with, and so lose information into the environment. Quantum Darwinism, and its more stringent cousins Strong Quantum Darwinism and Spectrum Broadcast Structures, seek to explain how this information loss is achieved in such a way as to be objective, classical and redundant. However there remains questions as to how the structure of the environment, states and types of interactions can give rise to this redundant encoding. In this thesis, we collect the work of 3 of our papers, exploring these questions. First, we show how information from one environment can spread to another. Then we show how commutativity can play a role in the emergence of objectivity. Lastly, we move beyond a single, pure system to a more realistic bipartite one, with both classical and quantum correlations between the subsystems. We shall show how interactions between only these subsystems can mediate the redundancy of others, and how these can lower bound and upper bound other forms of interactions between said subsystems and the environment.

Oct 1, 20260 citations

1/2

systems only, and we hope will be useful in future objectivity experiments.

We investigate quantum objectivity in the boson-spin model, where a central harmonic oscillator interacts with a thermal bath of spin-

\frac{1}{2}

systems. We analyze how information about a continuous position variable can be encoded into discrete, finite-dimensional environments. More precisely, we study conditions under which the so-called spectrum broadcast structures can be formed in the model. These are multipartite quantum-state structures, representing a mode-refined form of decoherence. Working in the recoil-less limit, we use the Floquet theory to show that despite its apparent simplicity, the model has a rich structure with different regimes, depending on the motion of the central system. In one of them, the faithful encoding of the position and hence objectivity are impossible irrespectively of the resources used. In another, large enough collections of spins will faithfully encode the position information. We derive the characteristic length scales, corresponding to decoherence and precision of the encoding.