216 research outputs found
Second moment of the Husimi distribution as a measure of complexity of quantum states
We propose the second moment of the Husimi distribution as a measure of
complexity of quantum states. The inverse of this quantity represents the
effective volume in phase space occupied by the Husimi distribution, and has a
good correspondence with chaoticity of classical system. Its properties are
similar to the classical entropy proposed by Wehrl, but it is much easier to
calculate numerically. We calculate this quantity in the quartic oscillator
model, and show that it works well as a measure of chaoticity of quantum
states.Comment: 25 pages, 10 figures. to appear in PR
Quantum Copying: Beyond the No-Cloning Theorem
We analyze to what extent it is possible to copy arbitrary states of a
two-level quantum system. We show that there exists a "universal quantum
copying machine", which approximately copies quantum mechanical states in such
a way that the quality of its output does not depend on the input. We also
examine a machine which combines a unitary transformation with a selective
measurement to produce good copies of states in a neighborhood of a particular
state. We discuss the problem of measurement of the output states.Comment: RevTex, 26 pages, to appear in Physical Review
Probability distributions consistent with a mixed state
A density matrix may be represented in many different ways as a
mixture of pure states, \rho = \sum_i p_i |\psi_i\ra \la \psi_i|. This paper
characterizes the class of probability distributions that may appear in
such a decomposition, for a fixed density matrix . Several illustrative
applications of this result to quantum mechanics and quantum information theory
are given.Comment: 6 pages, submitted to Physical Review
Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
Wehrl used Glauber coherent states to define a map from quantum density
matrices to classical phase space densities and conjectured that for Glauber
coherent states the mininimum classical entropy would occur for density
matrices equal to projectors onto coherent states. This was proved by Lieb in
1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for
every angular momentum . This conjecture is proved here. We also recall our
1991 extension of the Wehrl map to a quantum channel from to , with corresponding to the Wehrl map to classical densities.
For each and we show that the minimal output entropy for
these channels occurs for a coherent state. We also show that coherent
states both Glauber and Bloch minimize any concave functional, not just
entropy.Comment: Version 2 only minor change
Negative entropy and information in quantum mechanics
A framework for a quantum mechanical information theory is introduced that is
based entirely on density operators, and gives rise to a unified description of
classical correlation and quantum entanglement. Unlike in classical (Shannon)
information theory, quantum (von Neumann) conditional entropies can be negative
when considering quantum entangled systems, a fact related to quantum
non-separability. The possibility that negative (virtual) information can be
carried by entangled particles suggests a consistent interpretation of quantum
informational processes.Comment: 4 pages RevTeX, 2 figures. Expanded discussion of quantum
teleportation and superdense coding, and minor corrections. To appear in
Phys. Rev. Let
Accessibility of physical states and non-uniqueness of entanglement measure
Ordering physical states is the key to quantifying some physical property of
the states uniquely. Bipartite pure entangled states are totally ordered under
local operations and classical communication (LOCC) in the asymptotic limit and
uniquely quantified by the well-known entropy of entanglement. However, we show
that mixed entangled states are partially ordered under LOCC even in the
asymptotic limit. Therefore, non-uniqueness of entanglement measure is
understood on the basis of an operational notion of asymptotic convertibility.Comment: 8 pages, 1 figure. v2: main result unchanged but presentation
extensively changed. v3: figure added, minor correction
A classical analogue of entanglement
We show that quantum entanglement has a very close classical analogue, namely
secret classical correlations. The fundamental analogy stems from the behavior
of quantum entanglement under local operations and classical communication and
the behavior of secret correlations under local operations and public
communication. A large number of derived analogies follow. In particular
teleportation is analogous to the one-time-pad, the concept of ``pure state''
exists in the classical domain, entanglement concentration and dilution are
essentially classical secrecy protocols, and single copy entanglement
manipulations have such a close classical analog that the majorization results
are reproduced in the classical setting. This analogy allows one to import
questions from the quantum domain into the classical one, and vice-versa,
helping to get a better understanding of both. Also, by identifying classical
aspects of quantum entanglement it allows one to identify those aspects of
entanglement which are uniquely quantum mechanical.Comment: 13 pages, references update
Distinguishability of States and von Neumann Entropy
Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with
prior probabilities p_j respectively. We show that it is possible to increase
all of the pairwise overlaps || i.e. make each constituent pair
of the states more parallel (while keeping the prior probabilities the same),
in such a way that the von Neumann entropy S is increased, and dually, make all
pairs more orthogonal while decreasing S. We show that this phenomenon cannot
occur for ensembles in two dimensions but that it is a feature of almost all
ensembles of three states in three dimensions. It is known that the von Neumann
entropy characterises the classical and quantum information capacities of the
ensemble and we argue that information capacity in turn, is a manifestation of
the distinguishability of the signal states. Hence our result shows that the
notion of distinguishability within an ensemble is a global property that
cannot be reduced to considering distinguishability of each constituent pair of
states.Comment: 18 pages, Latex, 2 figure
Universal simulation of Hamiltonian dynamics for qudits
What interactions are sufficient to simulate arbitrary quantum dynamics in a
composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial
solution to this problem in the form of an efficient algorithm to simulate any
desired two-body Hamiltonian evolution using any fixed two-body entangling
N-qubit Hamiltonian, and local unitaries. We extend this result to the case
where the component systems have D dimensions. As a consequence we explain how
universal quantum computation can be performed with any fixed two-body
entangling N-qudit Hamiltonian, and local unitaries.Comment: 13 pages, an error in the "Pauli-Euclid-Gottesman Lemma" fixed, main
results unchange
The quantum capacity is properly defined without encodings
We show that no source encoding is needed in the definition of the capacity
of a quantum channel for carrying quantum information. This allows us to use
the coherent information maximized over all sources and and block sizes, but
not encodings, to bound the quantum capacity. We perform an explicit
calculation of this maximum coherent information for the quantum erasure
channel and apply the bound in order find the erasure channel's capacity
without relying on an unproven assumption as in an earlier paper.Comment: 19 pages revtex with two eps figures. Submitted to Phys. Rev. A.
Replaced with revised and simplified version, and improved references, etc.
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