International Journal of Quantum Information

We analyze the communication efficiency of quantum information transfer along unmodulated spin chains by computing the communication rates of various protocols. The effects of temporal correlations are discussed, showing that they can be exploited to boost the transmission efficiency.

In this work we study entanglement properties of a two-qubit system being affected by a classical noisy environment and coupled through exchange interaction. We study the dynamical generation of entanglement considering different initial conditions for the two-qubit system. We evaluate the rate at which entanglement is lost by calculating the concurrence as a function of time.

Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang–Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation's partial transposes is an algebra called the PPT algebra, which guides the construction of multipartite symmetric states. The virtual knot theory, having permutation as a virtual crossing, provides a topological language describing quantum computation as having permutation as a swap gate. In this paper, permutation's partial transpose is identified with an idempotent of the Temperley–Lieb algebra. The algebra generated by permutation and its partial transpose is found to be the Brauer algebra. The linear combinations of identity, permutation and its partial transpose can form various projectors describing tangles; braid representations; virtual braid representations underlying common solutions of the braid relation and Yang–Baxter equations; and virtual Temperley–Lieb algebra which is articulated from the graphical viewpoint. They lead to our drawing a picture called the ABPK diagram describing knot theory in terms of its corresponding algebra, braid group and polynomial invariant. The paper also identifies non-trivial unitary braid representations with universal quantum gates, derives a Hamiltonian to determine the evolution of a universal quantum gate, and further computes the Markov trace in terms of a universal quantum gate for a link invariant to detect linking numbers.

We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non–Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non–collective decoherence processes are studied. We give quantitative results for the Boltzmann gas and also for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice. These models can be simulated efficiently for systems of mesoscopic sizes (N ~ 10⁵).

Pseudo-telepathy is the most recent form of rejection of locality. Many of its properties have already been discovered: for instance, the minimal entanglement, as well as the minimal cardinality of the output sets, have been characterized. This paper contains two main results. First, we prove that no bipartite pseudo-telepathy game exists, in which one of the partners receives only two questions; as a corollary, we show that the minimal "input cardinality", that is, the minimal number of questions required in a bipartite pseudo-telepathy game, is 3 × 3. Second, we study the Bell-type inequality derived from the pseudo-telepathy game known as the Magic Square game: we demonstrate that it is a tight inequality for 3 inputs and 4 outputs on each side and discuss its weak resistance to noise.

New analytical formulas for the concurrence are introduced. A system of initially unentangled two two-level atoms entering a cavity successively and the effect of a nonlinear medium on the properties of their entanglement are studied. It is shown that a good periodical entanglement can be achieved with a weak nonlinear medium and low driving field, while the perfect is reached with high driving field and low or high parameters of nonlinearity.

A true quantum signature algorithm based on continuous-variable entanglement state is proposed. In the suggested algorithm, a key-pair, i.e. private signature key and public verification key, is generated based on a one-way function. By employing the signature key, a message state is encoded into a 2k-particle entangled state and a two-particle entangled state is prepared. The resulting states are exploited as a signature of the message state. The signature can be decoded under the verification key when it needs to be verified. Subsequently, a decoded message state and a two-particle entangled state are obtained. To compare the decoded states and the original states, a quantum circuit for comparing these states is exploited. Making use of measurement results of the quantum circuit one can judge the authenticity of the received signature. According to the security requirement of the signature scheme, the suggested algorithm has been proven to be theoretically secure by using the Shannon information theory.

Continuous-time quantum walk (CTQW) on a given graph is investigated using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of the Stieltjes function, namely, one can calculate the probability amplitudes only by taking the inverse laplace transform of the function iG_μ(is), where G_μ(x) is the Stieltjes function of the graph. The preference of this procedure is that there is no need to know the spectrum of the graph.

Unsorted database search problem is an important science and engineering problem. We proposed quantum algorithm to solve the problem by dividing the database binarily and then use a probabilistic verifier algorithm to determine if the item is within one part of the divided database. We analyzed the computational complexity of this algorithm, and found that in general, the number of steps is proportional to that in the standard Grover algorithm. However in some cases, it is less than that of the Grover algorithm.

It is a well–known fact that a quantum state |ψ(θ, ϕ)〉 is represented by a point on the Bloch sphere, characterized by two parameters θ and ϕ. Here in this work, we find out another impossible operation in quantum information theory. We name this impossibility as 'Impossibility of partial swapping of quantum information'. By this we mean that if two unknown quantum states are given at the input port, there exists no physical process, consistent with the principles of quantum mechanics, by which we can partially swap either of the two parameters θ and ϕ between these two quantum states. In this work, we provided the impossibility proofs for the qubits (i.e. the quantum states taken from two-dimensional Hilbert space) and this impossible operation can be shown to hold in higher dimensions also.

We give a simple proof of the impossibility of probabilistic exact 1 → 2 cloning for any three different states of a qubit. The simplicity of the proof is due to the use of a stronger version of no violation of the causality principle. The proof is also extended to higher-dimensional Hilbert space, but for a special ensemble of states.

We design a controlled-phase gate for linear optical quantum computing by using photodetectors that cannot resolve photon number. An intrinsic error-correction circuit corrects errors introduced by the detectors. Our controlled-phase gate has a 1/4 success probability. Recent development in cluster-state quantum computing has shown that a two-qubit gate with non-zero success probability can build an arbitrarily large cluster state only with polynomial overhead. Hence, it is possible to generate optical cluster states without number-resolving detectors and with polynomial overhead.

A question of theoretical and practical interest is how a quantum system may be measured indirectly by means of an ancilla that interacts with it, and furthermore, how a system of ancillas may be used to implement a coherent measurement of spatially separated qudits. We provide general circuits that can be used to implement such measurements. These circuits are relevant to quantum error correction, measurement-based quantum computation and Bell state discrimination across a quantum network involving multiple parties. The last mentioned problem is treated in detail. Our circuitry can also help to optimize the quantum communication complexity for performing measurements in distributed quantum computing.