Related papers: Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States

Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States

URL: http://arxiv.org/abs/2608.29933v1
Date: Sun, 30 Aug 2026 18:01:55 GMT
Title: Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
Abstract summary: We determine the entanglement structure of the conditional state obtained by measuring $m$ corresponding rungs in two identical copies.<n>We find that the entanglement entropy between the unmeasured parts of the two copies is independent of the initial state.<n>The success probability is given by $P_m=det C_Ldet(I_m-C_L)=det(C_LRC_RL)$, determined solely by the initial correlations.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We determine the exact entanglement structure of the conditional state obtained by measuring $m$ corresponding rungs ($m\leq N/2$) in two identical copies of an arbitrary half-filled free fermion Gaussian state and post-selecting the same normalized single-fermion state ($|ψ\rangle = u|10\rangle+v|01\rangle$, where 0 and 1 denote the fermion occupancy on each sites) on each rung. For $m<N/2$, the conditional wavefunction generally depends on the initial state. Nevertheless, whenever the selected outcome has nonzero probability, the state on the unmeasured sites remains Gaussian and factorizes exactly into $N-m$ different orthogonal modes including $m$ inter-copy entangling modes and $N-2m$ spectator modes localized in one copy. Consequently, the entanglement entropy between the unmeasured parts of the two copies is $S=m h_2(|v|^2)$, independent of the initial state, where $h_2(x)=-x\ln x-(1-x)\ln(1-x)$. The success probability is given by $P_m=\det C_L\det(I_m-C_L)=\det(C_{LR}C_{RL})$, determined solely by the initial correlations and independent of ($u$,$v$). Equal-weight Bell post-selection serves as a special case that achieves the maximal entanglement swapping.

Related papers

Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory [0.0]
Asymptotic matching predicts a bias-induced crossover in the region $1-2q=O( N/Nl n/2rfloor-1)$.<n>Activity-dependent control potential that cancels the conditional crosstalk mean restores the $Nn-1/ln N$ capacity for fixed $0q1/2$.
arXiv Detail & Related papers (2026-09-15T17:16:38Z)
Perfect State Transfer from a Localised Two-Excitation State to a Dicke State via Static Spin-Network Hamiltonians [0.0]
I construct a family of time-independent, symmetric-preserving spin Hamiltonians that realises perfect state transfer.<n>The construction exploits an $S_N-2$ permutation symmetry acting on the initially unoccupied spins.<n>For every $N ge 4$ an odd $n$ can be chosen large enough that a real root with $z -2$ exists.
arXiv Detail & Related papers (2026-09-09T03:06:14Z)
Third-Order Local Randomized Measurements for Finite-size Entanglement Certification [0.0]
Entanglement is certified when its minimum eigenvalue $mathcalE_4()$ becomes negative.<n>We prove that all separable states satisfy $barmathfrakM()succeq0$, and that the sign of $mathcalE_4()$ can be inferred from single-copy randomized measurements.
arXiv Detail & Related papers (2026-04-14T18:00:02Z)
Tripartite information of free fermions: a universal entanglement coefficient from the sine kernel [51.56484100374058]
We study the tripartite information I_3 of free fermions on two-dimensional lattices partitioned into three adjacent strips of width w.<n>We find that g(z) has a unique zero at z* = 1.329 +/- 0.001: modes with k_F w z* violate monogamy of mutual information.<n>Two exact cancellations -- of the z ln z area-law terms and of the z2 terms -- are intrinsic to the I_3 combination.
arXiv Detail & Related papers (2026-03-03T15:39:35Z)
Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
arXiv Detail & Related papers (2025-07-15T13:44:14Z)
Conserved operators and exact conditions for pair condensation [0.0]
Condition $Adagger=tfrac12sum_i,jA_ijc_idaggerc_jdagger$ is a general pair creation operator.<n>Conditions can be cast as an eigenvalue equation for a modified two-body density matrix.
arXiv Detail & Related papers (2025-03-05T20:42:22Z)
On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [54.28350823319057]
This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T.<n>Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$.<n>Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
arXiv Detail & Related papers (2024-02-01T07:21:32Z)
A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
arXiv Detail & Related papers (2023-09-25T17:54:19Z)
Classifying fermionic states via many-body correlation measures [0.0]
We make progress in establishing the link between fermionic correlations and efficient computational physics methods.<n>We find a rigorous classification of states relative to $k$-fermion correlations, which admits a computational physics interpretation.
arXiv Detail & Related papers (2023-09-14T18:00:02Z)
Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
arXiv Detail & Related papers (2021-04-26T15:03:08Z)
Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
arXiv Detail & Related papers (2020-11-23T14:40:27Z)
Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
arXiv Detail & Related papers (2020-06-04T17:51:00Z)
Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
arXiv Detail & Related papers (2020-02-08T22:02:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.