20,108 research outputs found
Competing density-wave orders in a one-dimensional hard-boson model
We describe the zero-temperature phase diagram of a model of bosons,
occupying sites of a linear chain, which obey a hard-exclusion constraint: any
two nearest-neighbor sites may have at most one boson. A special case of our
model was recently proposed as a description of a ``tilted'' Mott insulator of
atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to
generate the transfer matrix of Baxter's hard-square model. Aided by exact
solutions of a number of special cases, and by numerical studies, we obtain a
phase diagram containing states with long-range density-wave order with period
2 and period 3, and also a floating incommensurate phase. Critical theories for
the various quantum phase transitions are presented. As a byproduct, we show
how to compute the Luttinger parameter in integrable theories with
hard-exclusion constraints.Comment: 16 page
Optimal State Discrimination Using Particle Statistics
We present an application of particle statistics to the problem of optimal
ambiguous discrimination of quantum states. The states to be discriminated are
encoded in the internal degrees of freedom of identical particles, and we use
the bunching and antibunching of the external degrees of freedom to
discriminate between various internal states. We show that we can achieve the
optimal single-shot discrimination probability using only the effects of
particle statistics. We discuss interesting applications of our method to
detecting entanglement and purifying mixed states. Our scheme can easily be
implemented with the current technology
The Computational Complexity of Linear Optics
We give new evidence that quantum computers -- moreover, rudimentary quantum
computers built entirely out of linear-optical elements -- cannot be
efficiently simulated by classical computers. In particular, we define a model
of computation in which identical photons are generated, sent through a
linear-optical network, then nonadaptively measured to count the number of
photons in each mode. This model is not known or believed to be universal for
quantum computation, and indeed, we discuss the prospects for realizing the
model using current technology. On the other hand, we prove that the model is
able to solve sampling problems and search problems that are classically
intractable under plausible assumptions. Our first result says that, if there
exists a polynomial-time classical algorithm that samples from the same
probability distribution as a linear-optical network, then P^#P=BPP^NP, and
hence the polynomial hierarchy collapses to the third level. Unfortunately,
this result assumes an extremely accurate simulation. Our main result suggests
that even an approximate or noisy classical simulation would already imply a
collapse of the polynomial hierarchy. For this, we need two unproven
conjectures: the "Permanent-of-Gaussians Conjecture", which says that it is
#P-hard to approximate the permanent of a matrix A of independent N(0,1)
Gaussian entries, with high probability over A; and the "Permanent
Anti-Concentration Conjecture", which says that |Per(A)|>=sqrt(n!)/poly(n) with
high probability over A. We present evidence for these conjectures, both of
which seem interesting even apart from our application. This paper does not
assume knowledge of quantum optics. Indeed, part of its goal is to develop the
beautiful theory of noninteracting bosons underlying our model, and its
connection to the permanent function, in a self-contained way accessible to
theoretical computer scientists.Comment: 94 pages, 4 figure
Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions
In contrast to classical physics, quantum mechanics divides particles into
two classes-bosons and fermions-whose exchange statistics dictate the dynamics
of systems at a fundamental level. In two dimensions quasi-particles known as
'anyons' exhibit fractional exchange statistics intermediate between these two
classes. The ability to simulate and observe behaviour associated to
fundamentally different quantum particles is important for simulating complex
quantum systems. Here we use the symmetry and quantum correlations of entangled
photons subjected to multiple copies of a quantum process to directly simulate
quantum interference of fermions, bosons and a continuum of fractional
behaviour exhibited by anyons. We observe an average similarity of 93.6\pm0.2%
between an ideal model and experimental observation. The approach generalises
to an arbitrary number of particles and is independent of the statistics of the
particles used, indicating application with other quantum systems and large
scale application.Comment: 10 pages, 5 figure
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