Vol.3 No. 6
November 1,
2003
Research and
Review Articles:
Security bounds in quantum cryptography using dlevel systems
(pp563580)
A. Acin, N. Gisin and V. Scarani
We analyze the security of quantum
cryptography schemes for dlevel systems using 2 or d+1
maximally conjugated bases, under individual eavesdropping attacks based
on cloning machines and measurement after the basis reconciliation. We
consider classical advantage distillation protocols, that allow to
extract a key even in situations where the mutual information between
the honest parties is smaller than the eavesdropper's information. In
this scenario, advantage distillation protocols are shown to be as
powerful as quantum distillation: key distillation is possible using
classical techniques if and only if the corresponding state in the
entanglement based protocol is distillable.
Uncloneable encryption
(pp581602)
D. Gottesman
Quantum states cannot be cloned. I show how to extend this property to
classical messages encoded using quantum states, a task I call ``uncloneable
encryption.'' An uncloneable encryption scheme has the property that an
eavesdropper Eve not only cannot read the encrypted message, but she
cannot copy it down for later decoding. She could steal it, but then the
receiver Bob would not receive the message, and would thus be alerted
that something was amiss. I prove that any authentication scheme for
quantum states acts as a secure uncloneable encryption scheme.
Uncloneable encryption is also closely related to quantum key
distribution (QKD), demonstrating a close connection between
cryptographic tasks for quantum states and for classical messages. Thus,
studying uncloneable encryption and quantum authentication allows for
some modest improvements in QKD protocols. While the main results apply
to a onetime key with unconditional security, I also show uncloneable
encryption remains secure with a pseudorandom key. In this case, to
defeat the scheme, Eve must break the computational assumption behind
the pseudorandom sequence before Bob receives the message, or her
opportunity is lost. This means uncloneable encryption can be used in a
noninteractive setting, where QKD is not available, allowing Alice and
Bob to convert a temporary computational assumption into a permanently
secure message.
Proposal for realization of a Toffoli gate via
cavityassisted atomic collision
(pp603610)
H. Ollivier and P. Milman
Cavity QED is a versatile tool to explore small scale quantum
information processing. Within this setting, we describe a particular
protocol for implementing a Toffoli gate with Rydberg atoms and a cavity
field. Our scheme uses both resonant and non
resonant interactions, and in particular a cavity assisted atomic
collision. The experimental feasibility of the protocol is carefully
analyzed with the help of numerical simulations and takes into account
the decoherence process. Moreover, we show that our protocol is optimal
within the constraints imposed by the experimental setting.
On mixing in continuoustime quantum walks
on some circulant
graphs
(pp611618)
A. Ahmadi, R. Belk, C. Tamon and
C. Wendler
Classical random walks on wellbehaved graphs are rapidly mixing towards
the uniform distribution. Moore and Russell showed that the
continuoustime quantum walk on the hypercube is instantaneously uniform
mixing. We show that the continuoustime quantum walks on other
wellbehaved graphs do not exhibit
this uniform mixing. We prove that the only graphs amongst balanced
complete multipartite graphs that have the instantaneous exactly uniform
mixing property are the complete graphs on two, three and four vertices,
and the cycle graph on four vertices. Our proof exploits the circulant
structure of these graphs. Furthermore, we conjecture that most complete
cycles and Cayley graphs of the symmetric group lack this mixing
property as well.
An observable measure of entanglement
for pure states of multiqubit systems
(pp619626)
G. Brennen Recently, Meyer and
Wallach [Meyer and Wallach (2002), J. of Math. Phys., 43, pp. 4273]
proposed a measure of multiqubit entanglement that is a function on
pure states. We find that this function can be interpreted as a physical
quantity related to the average purity of the constituent qubits and
show how it can be observed in an efficient manner without the need for
full quantum state tomography. A possible realization is described for
measuring the entanglement of a chain of atomic qubits trapped in a 3D
optical lattice.
Entanglement of individual photon and atomic ensembles
(pp627634)
G.P. Guo and G.C. Guo Here we
present an experimentally feasible scheme to entangle flying qubit
(individual photon with polarization modes) and stationary qubit (atomic
ensembles with longlived collective excitations). This entanglement
integrating two different species can act as a critical element for the
coherent transfer of quantum information between flying and stationary
qubits. The entanglement degree can be also adjusted expediently with
linear optics. Furthermore, the present scheme can be modified to
generate this entanglement in a way eventready, with the employment of
a pair of entangled photons. And then successful preparation can be
unambiguously heralded by coincident between two singlephoton
detectors. Its application for individual photons quantum memory is also
analyzed. The physical requirements of all those preparation and
applications processing are moderate, and well fit the present
technique.
Two
QCMAcomplete problems
(pp635643)
P. Wocjan, D. Janzing and Th. Beth
QMA and QCMA are possible quantum analogues of the complexity class NP.
In QMA the proof is a quantum state and the verification is a quantum
circuit. In contrast, in QCMA the proof is restricted to be a classical
state. It is not known whether QMA strictly contains QCMA. Here we show
that two known QMAcomplete problems can be modified to QCMAcomplete
problems in a natural way: (1) Deciding whether a 3local Hamiltonian
has low energy states (with energy smaller than a given value) that can
be prepared with at most k elementary gates is QCMAcomplete,
whereas it is QMAcomplete when the restriction on the complexity of
preparation is dropped. (2) Deciding whether a (classically described)
quantum circuit does
not act as the identity on all basis states is QCMAcomplete. It
is QMAcomplete to decide whether it does not act on all states
as the identity.
Authors Index of Vol.3 (pp644645)
Titles Index of Vol.3 (pp646646)
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