357 research outputs found
Quantum Clock Synchronization: a Multi-Party Protocol
We present a multi-party quantum clock synchronization protocol that utilizes
shared prior entanglement and broadcast of classical information to synchronize
spatially separated clocks. Notably, it is necessary only for any one party to
publish classical information. Consequently, the efficacy of the method is
independent of the relative location of the parties. The suggested protocol is
robust and does not require precise sequencing of procedural steps.Comment: 3 page
A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
Two quantum information processing protocols are said to be dual under
resource reversal if the resources consumed (generated) in one protocol are
generated (consumed) in the other. Previously known examples include the
duality between entanglement concentration and dilution, and the duality
between coherent versions of teleportation and super-dense coding. A quantum
feedback channel is an isometry from a system belonging to Alice to a system
shared between Alice and Bob. We show that such a resource may be reversibly
decomposed into a perfect quantum channel and pure entanglement, generalizing
both of the above examples. The dual protocols responsible for this
decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum
reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf''
protocol (FQSW), a generalization of the recently discovered ``quantum state
merging'', is related to FF by source-channel duality, and to FQRS by time
reversal duality, thus forming a triangle of dualities. The source-channel
duality is identified as the origin of the previously poorly understood
``mother-father'' duality. Due to a symmetry breaking, the dualities extend
only partially to classical information theory.Comment: 5 pages, 5 figure
Towards a geometrical interpretation of quantum information compression
Let S be the von Neumann entropy of a finite ensemble E of pure quantum
states. We show that S may be naturally viewed as a function of a set of
geometrical volumes in Hilbert space defined by the states and that S is
monotonically increasing in each of these variables. Since S is the Schumacher
compression limit of E, this monotonicity property suggests a geometrical
interpretation of the quantum redundancy involved in the compression process.
It provides clarification of previous work in which it was shown that S may be
increased while increasing the overlap of each pair of states in the ensemble.
As a byproduct, our mathematical techniques also provide a new interpretation
of the subentropy of E.Comment: 11 pages, latex2
Universal Quantum Information Compression
Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).Comment: RevTex 4 page
On quantum coding for ensembles of mixed states
We consider the problem of optimal asymptotically faithful compression for
ensembles of mixed quantum states. Although the optimal rate is unknown, we
prove upper and lower bounds and describe a series of illustrative examples of
compression of mixed states. We also discuss a classical analogue of the
problem.Comment: 23 pages, LaTe
Quantum Key Distribution with Classical Bob
Secure key distribution among two remote parties is impossible when both are
classical, unless some unproven (and arguably unrealistic)
computation-complexity assumptions are made, such as the difficulty of
factorizing large numbers. On the other hand, a secure key distribution is
possible when both parties are quantum.
What is possible when only one party (Alice) is quantum, yet the other (Bob)
has only classical capabilities? We present a protocol with this constraint,
and prove its robustness against attacks: we prove that any attempt of an
adversary to obtain information (and even a tiny amount of information)
necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe
Measuring the purity of a qubit state: entanglement estimation with fully separable measurements
Given a finite number of copies of a qubit state we compute the maximum
fidelity that can be attained using joint-measurement protocols for estimating
its purity. We prove that in the asymptotic limit,
separable-measurement protocols can be as efficient as the optimal
joint-measurement one if classical communication is used. This in turn shows
that the optimal estimation of the entanglement of a two-qubit state can also
be achieved asymptotically with fully separable measurements. The relationship
between our global Bayesian approach and the quantum Cramer-Rao bound is also
discussed.Comment: 5 pages, 1 figure, RevTeX, improved versio
Secure quantum key distribution with an uncharacterized source
We prove the security of the Bennett-Brassard (BB84) quantum key distribution
protocol for an arbitrary source whose averaged states are basis-independent, a
condition that is automatically satisfied if the source is suitably designed.
The proof is based on the observation that, to an adversary, the key extraction
process is equivalent to a measurement in the sigma_x-basis performed on a pure
sigma_z-basis eigenstate. The dependence of the achievable key length on the
bit error rate is the same as that established by Shor and Preskill for a
perfect source, indicating that the defects in the source are efficiently
detected by the protocol.Comment: 4 pages, 1 figure, REVTeX, minor revision
On the role of entanglement in quantum computational speed-up
For any quantum algorithm operating on pure states we prove that the presence
of multi-partite entanglement, with a number of parties that increases
unboundedly with input size, is necessary if the quantum algorithm is to offer
an exponential speed-up over classical computation. Furthermore we prove that
the algorithm can be classically efficiently simulated to within a prescribed
tolerance \eta even if a suitably small amount of global entanglement
(depending on \eta) is present. We explicitly identify the occurrence of
increasing multi-partite entanglement in Shor's algorithm. Our results do not
apply to quantum algorithms operating on mixed states in general and we discuss
the suggestion that an exponential computational speed-up might be possible
with mixed states in the total absence of entanglement. Finally, despite the
essential role of entanglement for pure state algorithms, we argue that it is
nevertheless misleading to view entanglement as a key resource for quantum
computational power.Comment: Main proofs simplified. A few further explanatory remarks added. 22
pages, plain late
Lossless quantum data compression and variable-length coding
In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.Comment: 16 pages, 5 figure
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