Mixed-State Entanglement from Local Randomized Measurements

Elben, Andreas; Kueng, Richard; Huang, Hsin-Yuan; Bijnen, Rick van; Kokail, Christian; Dalmonte, Marcello; Calabrese, Pasquale; Kraus, Barbara; Preskill, John; Zoller, P.; Vermersch, Benoît

doi:10.1103/physrevlett.125.200501

Cited by 253 publications

(296 citation statements)

References 62 publications

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“…A can be negative, all the diagonal elements in the Fock basis are ≥ 0 because the partial transpose leaves invariant all the elements on the diagonal and so they remain the same as those of ρ A which are ≥ 0. This is evident in the example (20) and it is the same for any particle number. Hence p(q) satisfies p(q) ≥ 0 and q p(q) = 1, as it should be for a probability measure.…”

Section: Imbalance Entanglement Via Bosonic Partial Transposesupporting

confidence: 56%

“…A , the Rényi negativities define two separate sequences for even and odd n. Then the natural way to exploit the replica trick is to obtain the negativity by considering the analytic continuation of the even sequence of R n e at n e → 1 [17,18] (which is different from R 1 = 1). The moments R n with integer n ≥ 2 can also be measured in experiments [19][20][21], but they are not entanglement monotones. The entanglement negativity and Rényi negativities have been used to characterise mixed states in various quantum systems such as in harmonic oscillator chains [22][23][24][25][26][27][28][29][30], quantum spin models [31][32][33][34][35][36][37][38][39][40][41][42][43][44], (1+1)d conformal and integrable field theories [17,18,[45][46][47][48][49][50][51][52], topologically ordered phases of matter in (2+1)d [53][54][55][56][57], out-of-equilibrium settings [20,…”

Section: Introductionmentioning

confidence: 99%

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Symmetry decomposition of negativity of massless free fermions

2021

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We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.

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Section: Imbalance Entanglement Via Bosonic Partial Transposesupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Symmetry decomposition of negativity of massless free fermions

2021

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“…But how should we choose our M Pauli measurements (P) in order to achieve Conf ε (O; P) ≤ δ/2? The randomized measurement toolbox [12,13,21,35,37]…”

Section: Randomized Pauli Measurementsmentioning

confidence: 99%

Efficient Estimation of Pauli Observables by Derandomization

2021

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“…As a last physical application, we show that our solution allows us to compute explicitly the full time evolution of the Rényi entropies after the quench. This is especially relevant in light of their accessibility in recent state-of-theart quantum simulation experiments [71][72][73][74][75]. By repeating the reasoning that led to Eq.…”

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confidence: 99%

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

2021

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We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.

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Mixed-State Entanglement from Local Randomized Measurements

Cited by 253 publications

References 62 publications

Symmetry decomposition of negativity of massless free fermions

Symmetry decomposition of negativity of massless free fermions

Efficient Estimation of Pauli Observables by Derandomization

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

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