Tal Mor

Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures

We apply the full power of modern electronic band-structure engineering and epitaxial heterostructures to design a transistor that can sense and control a single-donor electron spin. Spin-resonance transistors may form the technological basis for quantum information processing. One- and two-qubit operations are performed by applying a gate bias. The bias electric field pulls the electron wave function away from the dopant ion into layers of different alloy composition. Owing to the variation of the g factor (Si: g1.998,Ge:g1.563), this displacement changes the spin Zeeman energy, allowing single-qubit operations. By displacing the electron even further, the overlap with neighboring qubits is affected, which allows two-qubit operations. Certain silicon-germanium alloys allow a qubit spacing as large as 200 nm, which is well within the capabilities of current lithographic techniques. We discuss manufacturing limitations and issues regarding scaling up to a large size computer.

Quantum nonlocality without entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

Unextendible product bases and bound entanglement

An unextendible product basis( UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the subspace complementary to any UPB is a bound entangled state. We exhibit a tripartite 2 3 2 3 2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e., all three corresponding 2 3 4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local positive operator valued measurements and classical communication. [S0031-9007(99)09360-6]

A Proof of the Security of Quantum Key Distribution

We prove the security of theoretical quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages such that their security is also unaffected in the future.

Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

AbstractWe report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.

QUANTUM CRYPTOGRAPHIC NETWORK BASED ON QUANTUM MEMORIES

Quantum correlations between two particles show nonclassical properties that can be used for providing secure transmission of information. We present a quantum cryptographic system in which users store particles in a transmission center, where their quantum states are preserved using quantum memories. Correlations between the particles stored by two users are created upon request by projecting their product state onto a fully entangled state. Our system allows for secure communication between any pair of users who have particles in the same center. Unlike other quantum cryptographic systems, it can work without quantum channels and it is suitable for building a quantum cryptographic network. We also present a modified system with many centers. \textcopyright{} 1996 The American Physical Society.

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 two protocols with this constraint, and prove their 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.

Security of Quantum Cryptography against Collective Attacks

We present strong attacks against quantum key distribution schemes which use quantum memories and quantum gates to attack directly the final key. We analyze a specific attack of this type, for which we find the density matrices available to the eavesdropper and the optimal information which can be extracted from them. We prove security against this attack and discuss security against any attack allowed by the rules of quantum mechanics.

Algorithmic cooling and scalable NMR quantum computers

We present here algorithmic cooling (via polarization heat bath)—a powerful method for obtaining a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. Given that spin-half states represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the Shannons bound on data compression, by using a set of rapidly thermal-relaxing bits. Such auxiliary bits could be implemented by using spins that rapidly get into thermal equilibrium with the environment, e.g., electron spins. Interestingly, the interaction with the environment, usually a most undesired interaction, is used here to our benefit, allowing a cooling mechanism. Cooling spins to a very low temperature without cooling the environment could lead to a breakthrough in NMR experiments, and our “spin-refrigerating” method suggests that this is possible. The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices, and our spin-refrigerating method suggests that this problem can be resolved.

A new universal and fault-tolerant quantum basis

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists only of two single-qubit gates (Hadamard and 1=4 z ), and one two-qubit gate (Controlled-NOT). Moreover, a new general method for fault-tolerant implementation of quantum gates like Toffoli is introduced. This method is a generalization of the methods suggested by Shor (Proc. FOCS’96, 1996, p. 56) and later by Knill et al. (Proc. Roy. Soc. London Ser. A 454 (1998) 365).