57,720 research outputs found
Quantum states far from the energy eigenstates of any local Hamiltonian
What quantum states are possible energy eigenstates of a many-body
Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of
the identity, and L-local, in the sense of containing interaction terms
involving at most L bodies, for some fixed L. We construct quantum states \psi
which are ``far away'' from all the eigenstates E of any non-trivial L-local
Hamiltonian, in the sense that |\psi-E| is greater than some constant lower
bound, independent of the form of the Hamiltonian.Comment: 4 page
Separable states are more disordered globally than locally
A remarkable feature of quantum entanglement is that an entangled state of
two parties, Alice (A) and Bob (B), may be more disordered locally than
globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is
known that satisfaction of this inequality implies that a state is
non-separable. In this paper we prove the stronger result that for separable
states the vector of eigenvalues of the density matrix of system AB is
majorized by the vector of eigenvalues of the density matrix of system A alone.
This gives a strong sense in which a separable state is more disordered
globally than locally and a new necessary condition for separability of
bipartite states in arbitrary dimensions. We also investigate the extent to
which these conditions are sufficient to characterize separability, exhibiting
examples that show separability cannot be characterized solely in terms of the
local and global spectra of a state. We apply our conditions to give a simple
proof that non-separable states exist sufficiently close to the completely
mixed state of qudits.Comment: 4 page
Fault-Tolerant Quantum Computation via Exchange interactions
Quantum computation can be performed by encoding logical qubits into the
states of two or more physical qubits, and controlling a single effective
exchange interaction and possibly a global magnetic field. This "encoded
universality" paradigm offers potential simplifications in quantum computer
design since it does away with the need to perform single-qubit rotations. Here
we show that encoded universality schemes can be combined with quantum error
correction. In particular, we show explicitly how to perform fault-tolerant
leakage correction, thus overcoming the main obstacle to fault-tolerant encoded
universality.Comment: 5 pages, including 1 figur
Entanglement, quantum phase transitions, and density matrix renormalization
We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying
remark
The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
In this Letter we show that an arbitrarily good approximation to the
propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may
be obtained with polynomial computational resources in n and the error
\epsilon, and exponential resources in |t|. Our proof makes use of the finitely
correlated state/matrix product state formalism exploited by numerical
renormalisation group algorithms like the density matrix renormalisation group.
There are two immediate consequences of this result. The first is that the
Vidal's time-dependent density matrix renormalisation group will require only
polynomial resources to simulate 1D quantum spin systems for logarithmic |t|.
The second consequence is that continuous-time 1D quantum circuits with
logarithmic |t| can be simulated efficiently on a classical computer, despite
the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen
Frustration, interaction strength and ground-state entanglement in complex quantum systems
Entanglement in the ground state of a many-body quantum system may arise when
the local terms in the system Hamiltonian fail to commute with the interaction
terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy
between ground-state entanglement and the phenomenon of frustration in spin
systems. In particular, we prove that the amount of ground-state entanglement
is bounded above by a measure of the extent to which interactions frustrate the
local terms in the Hamiltonian. As a corollary, we show that the amount of
ground-state entanglement is bounded above by a ratio between parameters
characterizing the strength of interactions in the system, and the local energy
scale. Finally, we prove a qualitatively similar result for other energy
eigenstates of the system.Comment: 11 pages, 3 figure
The spatial relation between the event horizon and trapping horizon
The relation between event horizons and trapping horizons is investigated in
a number of different situations with emphasis on their role in thermodynamics.
A notion of constant change is introduced that in certain situations allows the
location of the event horizon to be found locally. When the black hole is
accreting matter the difference in area between the two different horizons can
be many orders of magnitude larger than the Planck area. When the black hole is
evaporating the difference is small on the Planck scale. A model is introduced
that shows how trapping horizons can be expected to appear outside the event
horizon before the black hole starts to evaporate. Finally a modified
definition is introduced to invariantly define the location of the trapping
horizon under a conformal transformation. In this case the trapping horizon is
not always a marginally outer trapped surface.Comment: 16 pages, 1 figur
Theoretical Setting of Inner Reversible Quantum Measurements
We show that any unitary transformation performed on the quantum state of a
closed quantum system, describes an inner, reversible, generalized quantum
measurement. We also show that under some specific conditions it is possible to
perform a unitary transformation on the state of the closed quantum system by
means of a collection of generalized measurement operators. In particular,
given a complete set of orthogonal projectors, it is possible to implement a
reversible quantum measurement that preserves the probabilities. In this
context, we introduce the concept of "Truth-Observable", which is the physical
counterpart of an inner logical truth.Comment: 11 pages. More concise, shortened version for submission to journal.
References adde
A holographic proof of the strong subadditivity of entanglement entropy
When a quantum system is divided into subsystems, their entanglement
entropies are subject to an inequality known as "strong subadditivity". For a
field theory this inequality can be stated as follows: given any two regions of
space and , . Recently, a
method has been found for computing entanglement entropies in any field theory
for which there is a holographically dual gravity theory. In this note we give
a simple geometrical proof of strong subadditivity employing this holographic
prescription.Comment: 9 pages, 3 figure
Quantum computation with unknown parameters
We show how it is possible to realize quantum computations on a system in
which most of the parameters are practically unknown. We illustrate our results
with a novel implementation of a quantum computer by means of bosonic atoms in
an optical lattice. In particular we show how a universal set of gates can be
carried out even if the number of atoms per site is uncertain.Comment: 3 figure
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