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arXiv:2605.08076

Unlocking vacuum entanglement

Andrew Steane, Haru Ishizaka

quant-phSubmitted May 8, 2026• Announced May 11, 2026• 0 citations
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Abstract

The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.

Comments
4 pages, 4 figs

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The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.
We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled Gaussian states discussed by Boteno and Reznik [Phys. Rev. A 67, 052311 (2003)]. We find that the resulting entangled mode-shape hierarchy shows a distinctive layered structure with well-defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We rederive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite-size regions is connected with the localization of the highest-frequency innermost modes.
Harmonic chains are used as a model in quantum information theory for ion traps and simple solid state systems. Entanglement is a quantum effect in which observations made on one object instantaneously affect measurement outcomes on the other. This study investigates interparticle entanglement in finite chains of coupled harmonic oscillators as a function of the vibrational modes, mode excitations, and bipartition of oscillators. The methods used and results extend previous work for the Gaussian ground state to excited states. Entanglement is analyzed by calculating the purity of the reduced density matrix of the combined wavefunctions of the oscillators in the chain, tracing over subensembles. Analytic and numerical results for a varying effective spring constants between the particles and number of particles in the chain are presented. Interesting correlations between the symmetries of the vibrational modes and their excitations, and the symmetries of the partitions were discovered. Results show that higher excitation numbers result in higher entanglement. Adding energy to the modes will never decrease entanglement, however, the relationship between energy and entanglement is not simple. Different combinations of mode energy excitations will produce the same entanglement, even if the total energy of the system differs. Patterns indicate that the combination of symmetry in mode shapes and partition determines excitation number purity equivalence classes.
Decoherence remains one of the most serious challenges to the implementation of quantum technology. It appears as a result of the transformation over time of a quantum superposition state into a classical mixture due to the quantum system interacting with the environment. Since quantum systems are never completely isolated from their environment, decoherence therefore cannot be avoided in realistic situations. Decoherence has been extensively studied, mostly theoretically, because it has many important implications in quantum technology, such as in the fields of quantum information processing, quantum communication, and quantum computation. Here we report a novel experimental scheme on the study of decoherence of a two-mode squeezed vacuum state via its second harmonic generation signal. Our scheme can directly extract the decoherence of the phase-sensitive quantum correlation $\ensuremath{\langle}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}\ensuremath{\rangle}$ between two entangled modes aaa and bbb. Such a correlation is the most important characteristic of a two-mode squeezed state. More importantly, this is an experimental study on the decoherence effect of a squeezed vacuum state, which has been rarely investigated.
Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.
Mode entanglement in a two-mode squeezed state is studied. The entanglement spectrum is derived and interpreted as Boltzmann coefficients of harmonic oscillator eigenstates at thermal equilibrium. The effective temperature is expressed in terms of squeezing parameters and is equal to zero when the state is unsqueezed and increases without bound as the state is infinitely squeezed. It is demonstrated that the reduced density operator can be identified as a canonical ensemble of single harmonic oscillator at some effective temperature Te. The Renyi entanglement entropy is calculated and found to increase without bound as the squeezing parameter increases. The single-copy entanglement, which is a limiting value of the Renyi entropy, is interpreted as a partition function.