arXiv subjects

Aakash Marthandan

Publications and source records attributed to Aakash Marthandan.

3 recordsLinked to original sources

arXiv2025

Modular Hamiltonians for future-perturbed states

We develop a perturbative understanding of the modular Hamiltonian for a 2D CFT, divided into left and right half-spaces, with a weak local perturbation inserted in the future wedge. A formal perturbation series for the modular Hamiltonian is available, but must be properly interpreted in quantum field theory. We work inside correlation functions with spectator operators, and introduce a prescription for defining complex modular flow via analytic continuation to properly resolve singularities. From the correlators, we extract an operator expression for the modular Hamiltonian. It takes the form of a local operator in the future wedge plus contact terms with an unconventional singularity structure. Thanks to this structure the KMS conditions are satisfied, which independently establishes the validity of the results. Similar techniques apply to perturbations inserted in the past wedge. We mention various future directions, including an all-orders speculation for the excited state modular Hamiltonian.

hep-th↗

arXiv2025

Entanglement groups for mixed states

We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $\rho_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under conjugation, leaves $\rho_{AB}$ invariant. The entanglement group is a quotient of the stabilizer group, in which one-party stabilizers are considered trivial. This definition relates the entanglement of a density matrix to the entanglement of its purification. We give general properties of entanglement groups for mixed states, then discuss special properties for separable states. For a separable state, the entanglement group may be non-trivial. However it can only arise from multi-party entanglement with the purifying system.

quant-ph↗

arXiv2023

Entanglement groups

We propose to define entanglement in terms of local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a characterization of entanglement in terms of groups. We refer to these as entanglement groups, and we refer to this notion as $g$-entanglement. We discuss the physical meaning of entanglement groups and contrast $g$-entanglement with other, more conventional definitions of entanglement. For pure states, entanglement groups are constructed as certain quotients of the stabilizer group and its subgroups. For mixed states, entanglement groups can be constructed from stabilizers of the purification. We analyze the structure of entanglement groups, show that they have properties which correspond to monogamy of entanglement, and explore the restrictions placed by separability. We show that $g$-entanglement underlies several well-known quantum tasks.

quant-ph↗