We investigate universal entanglement properties inherent to superpositions of randomized states. We find that an $m$ -fold superposition of typical states may be classified into two distinct entanglement classes via the 2nd Rényi entropy density $s_2$ . The maximally entangled regime is defined by $s_2 \sim \ln (2)$ , for which superposition adds no additional entanglement. The sub-maximally entangled regime, $s_2<\ln 2$ , instead constrains the reduced density matrices of independent components to be orthogonal in the thermodynamic limit, which fixes the entanglement of the superposition to a logarithmic enhancement $ΔS(m)=\ln (m)$ . As a consequence, an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement. We explicitly calculate $s_2$ and the logarithmic enhancement, and demonstrate orthogonality for two canonical examples of the sub-maximally entangled regime (superpositions of pure Gaussian states and of random matrix-product states). We also examine the entanglement of superpositions of random stabilizer states, and discuss their relaxation to the Haar limit.We investigate universal entanglement properties inherent to superpositions of randomized states. We find that an $m$-fold superposition of typical states may be classified into two distinct entanglement classes via the 2nd Rényi entropy density $s_2$. The maximally entangled regime is defined by $s_2 \sim \ln (2)$, for which superposition adds no additional entanglement. The sub-maximally entangled regime, $s_2<\ln 2$, instead constrains the reduced density matrices of independent components to be orthogonal in the thermodynamic limit, which fixes the entanglement of the superposition to a logarithmic enhancement $ΔS(m)=\ln (m)$. As a consequence, an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement. We explicitly calculate $s_2$ and the logarithmic enhancement, and demonstrate orthogonality for two canonical examples of the sub-maximally entangled regime (superpositions of pure Gaussian states and of random matrix-product states). We also examine the entanglement of superpositions of random stabilizer states, and discuss their relaxation to the Haar limit.

quant-pharXiv:2607.06474Jul 8, 20260 citations

Universal maximally entangled states

M. Revzen

Quantum Studies Mathematics and FoundationsSep 23, 20142 citations

Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

Alex Monràs, Fabrizio Illuminati

We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within $d$ -dimensional cutoff subspaces ($d\ensuremath{\leqslant}6$) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within $d$-dimensional cutoff subspaces ($d\ensuremath{\leqslant}6$) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.

arXiv:1010.0442Physical Review AJan 24, 201192 citations

Mixtures of maximally entangled pure states

M. Flores, Eric A. Galapon

arXiv:1512.05539Annals of PhysicsJun 7, 20164 citations

ENTANGLEMENT FRUSTRATION IN MULTIMODE GAUSSIAN STATES

Cosmo Lupo, Stefano Mancini, Paolo Facchi A +2 more

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low- and high-energy limits.Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low- and high-energy limits.

arXiv:1110.3725International Journal of Geometric Methods in Modern PhysicsMar 1, 20122 citations

Preservers of maximally entangled states

Edward Poon

Linear Algebra and its ApplicationsMar 26, 20147 citations

We investigate universal entanglement properties inherent to superpositions of randomized states. We find that an

m

-fold superposition of typical states may be classified into two distinct entanglement classes via the 2nd Rényi entropy density

s_2

. The maximally entangled regime is defined by

s_2 \sim \ln (2)

, for which superposition adds no additional entanglement. The sub-maximally entangled regime,

s_2<\ln 2

, instead constrains the reduced density matrices of independent components to be orthogonal in the thermodynamic limit, which fixes the entanglement of the superposition to a logarithmic enhancement

ΔS(m)=\ln (m)

. As a consequence, an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement. We explicitly calculate

s_2

and the logarithmic enhancement, and demonstrate orthogonality for two canonical examples of the sub-maximally entangled regime (superpositions of pure Gaussian states and of random matrix-product states). We also examine the entanglement of superpositions of random stabilizer states, and discuss their relaxation to the Haar limit.

d

-dimensional cutoff subspaces ($d\ensuremath{\leqslant}6$) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.