98 research outputs found
Commuting Quantum Circuits with Few Outputs are Unlikely to be Classically Simulatable
We study the classical simulatability of commuting quantum circuits with n
input qubits and O(log n) output qubits, where a quantum circuit is classically
simulatable if its output probability distribution can be sampled up to an
exponentially small additive error in classical polynomial time. First, we show
that there exists a commuting quantum circuit that is not classically
simulatable unless the polynomial hierarchy collapses to the third level. This
is the first formal evidence that a commuting quantum circuit is not
classically simulatable even when the number of output qubits is exponentially
small. Then, we consider a generalized version of the circuit and clarify the
condition under which it is classically simulatable. Lastly, we apply the
argument for the above evidence to Clifford circuits in a similar setting and
provide evidence that such a circuit augmented by a depth-1 non-Clifford layer
is not classically simulatable. These results reveal subtle differences between
quantum and classical computation.Comment: 19 pages, 6 figures; v2: Theorems 1 and 3 improved, proofs modifie
Quantum information can be negative
Given an unknown quantum state distributed over two systems, we determine how
much quantum communication is needed to transfer the full state to one system.
This communication measures the "partial information" one system needs
conditioned on it's prior information. It turns out to be given by an extremely
simple formula, the conditional entropy. In the classical case, partial
information must always be positive, but we find that in the quantum world this
physical quantity can be negative. If the partial information is positive, its
sender needs to communicate this number of quantum bits to the receiver; if it
is negative, the sender and receiver instead gain the corresponding potential
for future quantum communication. We introduce a primitive "quantum state
merging" which optimally transfers partial information. We show how it enables
a systematic understanding of quantum network theory, and discuss several
important applications including distributed compression, multiple access
channels and multipartite assisted entanglement distillation (localizable
entanglement). Negative channel capacities also receive a natural
interpretation
Detection of multipartite entanglement with two-body correlations
We show how to detect entanglement with criteria built from simple two-body
correlation terms. Since many natural Hamiltonians are sums of such correlation
terms, our ideas can be used to detect entanglement by energy measurement. Our
criteria can straightforwardly be applied for detecting different forms of
multipartite entanglement in familiar spin models in thermal equilibrium.Comment: 5 pages including 2 figures, LaTeX; for the proceedings of the DPG
spring meeting, Berlin, March 200
The Uncertainty Principle in the Presence of Quantum Memory
The uncertainty principle, originally formulated by Heisenberg, dramatically
illustrates the difference between classical and quantum mechanics. The
principle bounds the uncertainties about the outcomes of two incompatible
measurements, such as position and momentum, on a particle. It implies that one
cannot predict the outcomes for both possible choices of measurement to
arbitrary precision, even if information about the preparation of the particle
is available in a classical memory. However, if the particle is prepared
entangled with a quantum memory, a device which is likely to soon be available,
it is possible to predict the outcomes for both measurement choices precisely.
In this work we strengthen the uncertainty principle to incorporate this case,
providing a lower bound on the uncertainties which depends on the amount of
entanglement between the particle and the quantum memory. We detail the
application of our result to witnessing entanglement and to quantum key
distribution.Comment: 5 pages plus 12 of supplementary information. Updated to match the
journal versio
Experimental investigation of classical and quantum correlations under decoherence
It is well known that many operations in quantum information processing
depend largely on a special kind of quantum correlation, that is, entanglement.
However, there are also quantum tasks that display the quantum advantage
without entanglement. Distinguishing classical and quantum correlations in
quantum systems is therefore of both fundamental and practical importance. In
consideration of the unavoidable interaction between correlated systems and the
environment, understanding the dynamics of correlations would stimulate great
interest. In this study, we investigate the dynamics of different kinds of
bipartite correlations in an all-optical experimental setup. The sudden change
in behaviour in the decay rates of correlations and their immunity against
certain decoherences are shown. Moreover, quantum correlation is observed to be
larger than classical correlation, which disproves the early conjecture that
classical correlation is always greater than quantum correlation. Our
observations may be important for quantum information processing.Comment: 7 pages, 4 figures, to appear in Nature Communication
Entropic Uncertainty Relations in Quantum Physics
Uncertainty relations have become the trademark of quantum theory since they
were formulated by Bohr and Heisenberg. This review covers various
generalizations and extensions of the uncertainty relations in quantum theory
that involve the R\'enyi and the Shannon entropies. The advantages of these
entropic uncertainty relations are pointed out and their more direct connection
to the observed phenomena is emphasized. Several remaining open problems are
mentionedComment: 35 pages, review pape
Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
Entanglement lies at the heart of quantum mechanics and in recent years has
been identified as an essential resource for quantum information processing and
computation. Creating highly entangled multi-particle states is therefore one
of the most challenging goals of modern experimental quantum mechanics,
touching fundamental questions as well as practical applications. Here we
report on the experimental realization of controlled collisions between
individual neighbouring neutral atoms trapped in the periodic potential of an
optical lattice. These controlled interactions act as an array of quantum gates
between neighbouring atoms in the lattice and their massively parallel
operation allows the creation of highly entangled states in a single
operational step, independent of the size of the system. In the experiment, we
observe a coherent entangling-disentangling evolution in the many-body system
depending on the phase shift acquired during the collision between neighbouring
atoms. This dynamics is indicative of highly entangled many-body states that
present novel opportunities for theory and experiment.Comment: 17 pages, including 5 figures, accepted for publication in Natur
Experimental investigation of the uncertainty principle in the presence of quantum memory
Heisenberg's uncertainty principle provides a fundamental limitation on an
observer's ability to simultaneously predict the outcome when one of two
measurements is performed on a quantum system. However, if the observer has
access to a particle (stored in a quantum memory) which is entangled with the
system, his uncertainty is generally reduced. This effect has recently been
quantified by Berta et al. [Nature Physics 6, 659 (2010)] in a new, more
general uncertainty relation, formulated in terms of entropies. Using entangled
photon pairs, an optical delay line serving as a quantum memory and fast,
active feed-forward we experimentally probe the validity of this new relation.
The behaviour we find agrees with the predictions of quantum theory and
satisfies the new uncertainty relation. In particular, we find lower
uncertainties about the measurement outcomes than would be possible without the
entangled particle. This shows not only that the reduction in uncertainty
enabled by entanglement can be significant in practice, but also demonstrates
the use of the inequality to witness entanglement.Comment: 8 pages, 4 figures, comments welcom
Scalable multi-particle entanglement of trapped ions
Among the various kinds of entangled states, the 'W state' plays an important
role as its entanglement is maximally persistent and robust even under particle
loss. Such states are central as a resource in quantum information processing
and multiparty quantum communication. Here we report the scalable and
deterministic generation of four-, five-, six-, seven- and eight-particle
entangled states of the W type with trapped ions. We obtain the maximum
possible information on these states by performing full characterization via
state tomography, using individual control and detection of the ions. A
detailed analysis proves that the entanglement is genuine. The availability of
such multiparticle entangled states, together with full information in the form
of their density matrices, creates a test-bed for theoretical studies of
multiparticle entanglement. Independently, -Greenberger-Horne-Zeilinger-
entangled states with up to six ions have been created and analysed in Boulder
Repeated Quantum Error Detection in a Surface Code
The realization of quantum error correction is an essential ingredient for
reaching the full potential of fault-tolerant universal quantum computation.
Using a range of different schemes, logical qubits can be redundantly encoded
in a set of physical qubits. One such scalable approach is based on the surface
code. Here we experimentally implement its smallest viable instance, capable of
repeatedly detecting any single error using seven superconducting qubits, four
data qubits and three ancilla qubits. Using high-fidelity ancilla-based
stabilizer measurements we initialize the cardinal states of the encoded
logical qubit with an average logical fidelity of 96.1%. We then repeatedly
check for errors using the stabilizer readout and observe that the logical
quantum state is preserved with a lifetime and coherence time longer than those
of any of the constituent qubits when no errors are detected. Our demonstration
of error detection with its resulting enhancement of the conditioned logical
qubit coherence times in a 7-qubit surface code is an important step indicating
a promising route towards the realization of quantum error correction in the
surface code.Comment: 12 pages, 11 figure
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