30,981 research outputs found
Languages of Quantum Information Theory
This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.Comment: 16 pages, REVTEX, typos corrected, references added and extende
Two-message quantum interactive proofs and the quantum separability problem
Suppose that a polynomial-time mixed-state quantum circuit, described as a
sequence of local unitary interactions followed by a partial trace, generates a
quantum state shared between two parties. One might then wonder, does this
quantum circuit produce a state that is separable or entangled? Here, we give
evidence that it is computationally hard to decide the answer to this question,
even if one has access to the power of quantum computation. We begin by
exhibiting a two-message quantum interactive proof system that can decide the
answer to a promise version of the question. We then prove that the promise
problem is hard for the class of promise problems with "quantum statistical
zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp
reduction from the QSZK-complete promise problem "quantum state
distinguishability" to our quantum separability problem. By exploiting Knill's
efficient encoding of a matrix description of a state into a description of a
circuit to generate the state, we can show that our promise problem is NP-hard
with respect to Cook reductions. Thus, the quantum separability problem (as
phrased above) constitutes the first nontrivial promise problem decidable by a
two-message quantum interactive proof system while being hard for both NP and
QSZK. We also consider a variant of the problem, in which a given
polynomial-time mixed-state quantum circuit accepts a quantum state as input,
and the question is to decide if there is an input to this circuit which makes
its output separable across some bipartite cut. We prove that this problem is a
complete promise problem for the class QIP of problems decidable by quantum
interactive proof systems. Finally, we show that a two-message quantum
interactive proof system can also decide a multipartite generalization of the
quantum separability problem.Comment: 34 pages, 6 figures; v2: technical improvements and new result for
the multipartite quantum separability problem; v3: minor changes to address
referee comments, accepted for presentation at the 2013 IEEE Conference on
Computational Complexity; v4: changed problem names; v5: updated references
and added a paragraph to the conclusion to connect with prior work on
separability testin
Spatial mode storage in a gradient echo memory
Three-level atomic gradient echo memory (lambda-GEM) is a proposed candidate
for efficient quantum storage and for linear optical quantum computation with
time-bin multiplexing. In this paper we investigate the spatial multimode
properties of a lambda-GEM system. Using a high-speed triggered CCD, we
demonstrate the storage of complex spatial modes and images. We also present an
in-principle demonstration of spatial multiplexing by showing selective recall
of spatial elements of a stored spin wave. Using our measurements, we consider
the effect of diffusion within the atomic vapour and investigate its role in
spatial decoherence. Our measurements allow us to quantify the spatial
distortion due to both diffusion and inhomogeneous control field scattering and
compare these to theoretical models.Comment: 11 pages, 9 figure
Monodromy analysis of the computational power of the Ising topological quantum computer
We show that all quantum gates which could be implemented by braiding of
Ising anyons in the Ising topological quantum computer preserve the n-qubit
Pauli group. Analyzing the structure of the Pauli group's centralizer, also
known as the Clifford group, for n\geq 3 qubits, we prove that the image of the
braid group is a non-trivial subgroup of the Clifford group and therefore not
all Clifford gates could be implemented by braiding. We show explicitly the
Clifford gates which cannot be realized by braiding estimating in this way the
ultimate computational power of the Ising topological quantum computer.Comment: 10 pages, 2 figures and 1 table; v2: one more reference added and
some typos corrected; Talk given at the VIII International Workshop "Lie
Theory and its Applications in Physics", 15-21 June 2009, Varna, Bulgari
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