Vol.2 No.1 Dec. 15, 2001 (print: Jan. 15,
2002)
Researches:
On the
classical character of control fields in quantum information processing
(pp113)
S.J. van Enk and
H.J. Kimble Control fields
in quantum information processing are almost by definition assumed to be
classical. In reality, however, when such a field is used to manipulate
the quantum state of qubits, the qubits always become slightly entangled
with the field. For quantum information processing this is an
undesirable property, as it precludes perfect quantum computing and
quantum communication. Here we consider the interaction of atomic qubits
with laser fields and quantify atomfield entanglement in various cases
of interest. We find that the entanglement decreases with the average
number of photons \bar{n} in a laser beam as $E\propto\log_2 \bar{n}/\bar{n}$
for $\bar{n}\rightarrow\infty$.
Quantum vernam
cipher
(pp1434)
D.
W. Leung
We discuss aspects of secure quantum
communication by proposing and analyzing a quantum analog of the Vernam
cipher (onetimepad). The quantum Vernam cipher uses entanglement as
the key to encrypt quantum information sent through an insecure quantum
channel. First, in sharp contrast with the classical Vernam cipher, the
quantum key can be recycled securely. We show that key recycling is
intrinsic to the quantum ciphertext, rather than using entanglement as
the key. Second, the scheme detects and corrects for arbitrary
transmission errors, and it does so using only local operations and
classical communication (LOCC) between the sender and the receiver. The
application to quantum message authentication is discussed. Quantum
secret sharing schemes with similar properties are characterized. We
also discuss two general issues, the relation between secret
communication and secret sharing, the classification of secure
communication protocols.
Counting,
fanout and the complexity of quantum ACC
(pp3565)
F. Green, S.
Homer, C. Moore, and C. Pollett
We propose definitions of QAC^0,
the quantum analog of the classical class AC^0 of constantdepth
circuits with AND and OR gates of arbitrary fanin, and QACC[q], the
analog of the class ACC[q] where Mod_q gates are also allowed. We
prove that parity or fanout allows us to construct quantum MOD_q gates
in constant depth for any q, so QACC[2] = QACC. More generally, we show
that for any q,p > 1, MOD_q is equivalent to MOD_p (up to constant depth
and polynomial size). This implies that QAC^0
with unbounded fanout gates, denoted QACwf^0, is the same as QACC[q] and QACC for all
q. Since \ACC[p] \ne ACC[q] whenever p and q are distinct primes, QACC[q]
is strictly more powerful than its classical counterpart, as is QAC^0 when fanout
is allowed. This adds to the growing list of quantum complexity classes
which are provably more powerful than their classical counterparts. We
also develop techniques for proving upper bounds for QACC in terms of related
language classes. We define classes of languages closely related to
QACC[2] and show that restricted versions of them can be simulated by
polynomialsize circuits. With further restrictions, language classes
related to QACC[2] operators can be simulated by classical threshold
circuits of polynomial size and constant depth.
Optimization
of coherent attacks in generalizations of the BB84 quantum bit
commitment protocol
(pp6696)
R.W.
Spekkens and T. Rudolph
It is well known that no quantum bit commitment
protocol is unconditionally secure. Nonetheless, there can be
nontrivial upper bounds on both Bob's probability of correctly
estimating Alice's commitment and Alice's probability of successfully
unveiling whatever bit she desires. In this paper, we seek to determine
these bounds for generalizations of the BB84 bit commitment protocol. In
such protocols, an honest Alice commits to a bit by randomly choosing a
state from a specified set and submitting this to Bob, and later unveils
the bit to Bob by announcing the chosen state, at which point Bob
measures the projector onto the state. Bob's optimal cheating strategy
can be easily deduced from well known results in the theory of quantum
state estimation. We show how to understand Alice's most general
cheating strategy, (which involves her submitting to Bob one half of an
entangled state) in terms of a theorem of Hughston, Jozsa and Wootters.
We also show how the problem of optimizing Alice's cheating strategy for
a fixed submitted state can be mapped onto a problem of state
estimation. Finally, using the Bloch ball representation of qubit
states, we identify the optimal coherent attack for a class of protocols
that can be implemented with just a single qubit. These results
provide a tight upper bound on Alice's probability of successfully
unveiling whatever bit she desires in the protocol proposed by Aharonov
et al., and lead us to identify a qubit protocol with even greater
security.
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