543 research outputs found
Quantum Brownian motion in a quasiperiodic potential
We consider a quantum particle subject to Ohmic dissipation, moving in a
bichromatic quasiperiodic potential. In a periodic potential the particle
undergoes a zero-temperature localization-delocalization transition as
dissipation strength is decreased. We show that the delocalized phase is absent
in the quasiperiodic case, even when the deviation from periodicity is
infinitesimal. Using the renormalization group, we determine how the effective
localization length depends on the dissipation. We show that {a similar problem
can emerge in} the strong-coupling limit of a mobile impurity moving in a
periodic lattice and immersed in a one-dimensional quantum gas.Comment: 5+6 pages, 1 figur
Localization-protected order in spin chains with non-Abelian discrete symmetries
We study the non-equilibrium phase structure of the three-state random
quantum Potts model in one dimension. This spin chain is characterized by a
non-Abelian symmetry recently argued to be incompatible with the
existence of a symmetry-preserving many-body localized (MBL) phase. Using exact
diagonalization and a finite-size scaling analysis, we find that the model
supports two distinct broken-symmetry MBL phases at strong disorder that either
break the clock symmetry or a chiral
symmetry. In a dual formulation, our results indicate the existence of a stable
finite-temperature topological phase with MBL-protected parafermionic end zero
modes. While we find a thermal symmetry-preserving regime for weak disorder,
scaling analysis at strong disorder points to an infinite-randomness critical
point between two distinct broken-symmetry MBL phases.Comment: 5 pages, 3 figures main text; 6 pages, 3 figures supplemental
material; Version 2 includes a corrected the form of the chiral order
parameter, and corresponding data, as well as larger system size numerics,
with no change to the phase structur
Particle-hole symmetry, many-body localization, and topological edge modes
We study the excited states of interacting fermions in one dimension with
particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a
combination of renormalization group methods and exact diagonalization. Absent
interactions, the entire many-body spectrum exhibits infinite-randomness
quantum critical behavior with highly degenerate excited states. We show that
though interactions are an irrelevant perturbation in the ground state, they
drastically affect the structure of excited states: even arbitrarily weak
interactions split the degeneracies in favor of thermalization (weak disorder)
or spontaneously broken particle-hole symmetry, driving the system into a
many-body localized spin glass phase (strong disorder). In both cases, the
quantum critical properties of the non-interacting model are destroyed, either
by thermal decoherence or spontaneous symmetry breaking. This system then has
the interesting and counterintuitive property that edges of the many-body
spectrum are less localized than the center of the spectrum. We argue that our
results rule out the existence of certain excited state symmetry-protected
topological orders.Comment: 9 pages. 7 figure
Measurement-induced phases of matter require feedback
We explore universality and phases of matter in hybrid quantum dynamics
combining chaotic time evolution and projective measurements. We develop a
unitary representation of measurements based on the Stinespring Theorem, which
we crucially identify with the time evolution of the system and measurement
apparatus, affording significant technical advantages and conceptual insight
into hybrid dynamics. We diagnose spectral properties in the presence of
measurements for the first time, along with standard, experimentally tractable
probes of phase structure, finding no nontrivial effects due to measurements in
the absence of feedback. We also establish that nonlinearity in the density
matrix is neither sufficient nor necessary to see a transition, and instead
identify utilization of the measurement outcomes (i.e., ``feedback'') as the
crucial ingredient. After reviewing the definition of a phase of matter, we
identify nontrivial orders in adaptive hybrid dynamics -- in which measurement
outcomes determine future unitary gates -- finding a genuine
measurement-induced absorbing-state phase transition in an adaptive quantum
East model. In general, we find that only deterministic and constrained
Haar-random dynamics with active feedback and without continuous symmetries can
realize genuine, measurement-induced phases of matter.Comment: 36 + 8 pages, 9 figures; v2 includes numerical simulations of
adaptive dynamics, clarifications throughou
Quantum teleportation implies symmetry-protected topological order
We constrain a broad class of teleportation protocols using insights from
locality. In the "standard" teleportation protocols we consider, all
outcome-dependent unitaries are Pauli operators conditioned on linear functions
of the measurement outcomes. We find that all such protocols involve preparing
a "resource state" exhibiting symmetry-protected topological (SPT) order with
Abelian protecting symmetry . The logical states are teleported between the edges of
the chain by measuring the corresponding string order parameters in the
bulk and applying outcome-dependent Paulis. Hence, this single class of
nontrivial SPT states is both necessary and sufficient for the standard
teleportation of qubits. We illustrate this result with several examples,
including a nonstabilizer hypergraph state.Comment: 33 pages, 8 figure
Locality and error correction in quantum dynamics with measurement
The speed of light sets a strict upper bound on the speed of information
transfer in both classical and quantum systems. In nonrelativistic systems, the
Lieb-Robinson Theorem imposes an emergent speed limit , establishing locality under unitary quantum dynamics and
constraining the time needed to perform useful quantum tasks. We extend the
Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the
general expectation that measurements can arbitrarily violate spatial locality,
we find at most an -fold enhancement to
the speed of quantum information , provided the outcomes of local
measurements are known; this holds even when classical communication is
instantaneous. Our bound is asymptotically optimal, and saturated by existing
measurement-based protocols. We tightly constrain the resource requirements for
quantum computation, error correction, teleportation, and generating entangled
resource states (Bell, GHZ, W, and spin-squeezed states) from short-range
entangled states. Our results impose limits on the use of measurements and
active feedback to speed up quantum information processing, resolve fundamental
questions about the nature of measurements in quantum dynamics, and constrain
the scalability of a wide range of proposed quantum technologies.Comment: 5 pages + 3 figures main text; 55 pages + 4 figures supplement; v3
supplement has overview section, clarified interpretation of main theorem,
additional bounds and protocol
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