From communication complexity to an entanglement spread area law in the
ground state of gapped local Hamiltonians
- URL: http://arxiv.org/abs/2004.15009v1
- Date: Thu, 30 Apr 2020 17:54:22 GMT
- Title: From communication complexity to an entanglement spread area law in the
ground state of gapped local Hamiltonians
- Authors: Anurag Anshu, Aram W. Harrow, Mehdi Soleimanifar
- Abstract summary: We make a connection between two seemingly different problems.
The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians.
The second problem is on the quantum communication complexity of testing bipartite states with EPR assistance.
- Score: 16.951941479979716
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we make a connection between two seemingly different problems.
The first problem involves characterizing the properties of entanglement in the
ground state of gapped local Hamiltonians, which is a central topic in quantum
many-body physics. The second problem is on the quantum communication
complexity of testing bipartite states with EPR assistance, a well-known
question in quantum information theory. We construct a communication protocol
for testing (or measuring) the ground state and use its communication
complexity to reveal a new structural property for the ground state
entanglement. This property, known as the entanglement spread, roughly measures
the ratio between the largest and the smallest Schmidt coefficients across a
cut in the ground state. Our main result shows that gapped ground states
possess limited entanglement spread across any cut, exhibiting an "area law"
behavior. Our result quite generally applies to any interaction graph with an
improved bound for the special case of lattices. This entanglement spread area
law includes interaction graphs constructed in [Aharonov et al., FOCS'14] that
violate a generalized area law for the entanglement entropy. Our construction
also provides evidence for a conjecture in physics by Li and Haldane on the
entanglement spectrum of lattice Hamiltonians [Li and Haldane, PRL'08]. On the
technical side, we use recent advances in Hamiltonian simulation algorithms
along with quantum phase estimation to give a new construction for an
approximate ground space projector (AGSP) over arbitrary interaction graphs.
Related papers
- Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions.
We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
arXiv Detail & Related papers (2024-07-09T14:04:11Z) - Comment on "Can Neural Quantum States Learn Volume-Law Ground States?" [44.99833362998488]
We show that suitably chosen NQS can learn ground states with volume-law entanglement both for spin and fermionic problems.
We argue that the setup utilized in the aforementioned letter reveals the inefficiency of non-fermionic NQS to learn fermionic states.
arXiv Detail & Related papers (2023-09-20T14:44:04Z) - Exploring Large-Scale Entanglement in Quantum Simulation [0.0]
Entanglement is a distinguishing feature of quantum many-body systems.
Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian.
arXiv Detail & Related papers (2023-05-31T18:00:01Z) - Estimating gate complexities for the site-by-site preparation of
fermionic vacua [0.0]
We study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians.
For one-dimensional systems, we find that two $N/2$-site ground states also share a large overlap with the $N$-site ground state everywhere except a region near the phase boundary.
arXiv Detail & Related papers (2022-07-04T19:45:14Z) - The frustration-free fully packed loop model [4.965221313169878]
We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes.
We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace.
We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
arXiv Detail & Related papers (2022-06-03T18:00:04Z) - Persistent homology of quantum entanglement [0.0]
We study the structure of entanglement entropy using persistent homology.
The inverse quantum mutual information between pairs of sites is used as a distance metric to form a filtered simplicial complex.
We also discuss the promising future applications of this modern computational approach, including its connection to the question of how spacetime could emerge from entanglement.
arXiv Detail & Related papers (2021-10-19T19:23:39Z) - Entanglement Spectroscopy and probing the Li-Haldane Conjecture in
Topological Quantum Matter [0.0]
Topological phases are characterized by their entanglement properties.
We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian.
arXiv Detail & Related papers (2021-10-08T06:13:51Z) - Long-distance entanglement of purification and reflected entropy in
conformal field theory [58.84597116744021]
We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy.
We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
arXiv Detail & Related papers (2021-01-29T19:00:03Z) - Entanglement and Complexity of Purification in (1+1)-dimensional free
Conformal Field Theories [55.53519491066413]
We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace.
We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
arXiv Detail & Related papers (2020-09-24T18:00:13Z) - Einselection from incompatible decoherence channels [62.997667081978825]
We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators.
We show that Fock states remain the most robust states to decoherence up to a critical coupling.
arXiv Detail & Related papers (2020-01-29T14:15:19Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.