Vol.3 No. 6  November 1, 2003
Research and Review Articles:
Security bounds in quantum cryptography using d-level systems  (pp563-580)
        A. Acin, N. Gisin and V. Scarani
We analyze the security of quantum cryptography schemes for d-level 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  (pp581-602)
        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 one-time 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 non-interactive 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 cavity-assisted atomic collision  (pp603-610)
        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 continuous-time quantum walks on some circulant graphs  (pp611-618)
        A. Ahmadi, R. Belk, C. Tamon and C. Wendler
Classical random walks on well-behaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that the continuous-time quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuous-time quantum walks on other well-behaved 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 multi-qubit systems  (pp619-626)
        G. Brennen
Recently, Meyer and Wallach [Meyer and Wallach (2002), J. of Math. Phys., 43, pp. 4273] proposed a measure of multi-qubit 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  (pp627-634)
        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 long-lived 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 event-ready, with the employment of a pair of entangled photons. And then successful preparation can be unambiguously heralded by coincident between two single-photon 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 QCMA-complete problems  (pp635-643)
        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 QMA-complete problems can be modified to QCMA-complete problems in a natural way: (1) Deciding whether a 3-local Hamiltonian has low energy states (with energy smaller than a given value) that can be prepared with at most k elementary gates is QCMA-complete, whereas it is QMA-complete 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 QCMA-complete. It is QMA-complete to decide whether it does not act on all states as the identity.

Authors Index of Vol.3  (pp644-645)
Titles Index of Vol.3  (pp646-646)

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