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We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the information on coin 1 state at target position only by at most two times of flipping operation. Based on quantum walks with two coins either on the line or on the N -circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins either on complete graphs or regular graphs, we can first implement perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer more general state. Moreover, the external control of coin operator during the transmitting process can be decreased greatly. Selecting coin 1 as the sender and coin 2 as the receiver, we also study how to realize generalized teleportation over long steps of walks by the above quantum walk models. Because quantum walks is an universal quantum computation model, our schemes may provide an universal platform for the design of quantum network and quantum computer.

What is the minimal number of elements in a rank-1 positiveoperator-valued measure (POVM) which can uniquely determine any pure state in d-dimensional Hilbert space H d ? The known result is that the number is no less than 3d − 2. We show that this lower bound is not tight except for d = 2 or 4. Then we give an upper bound of 4d−3. For d = 2, many rank-1 POVMs with four elements can determine any pure states in H2. For d = 3, we show eight is the minimal number by construction. For d = 4, the minimal number is in the set of {10, 11, 12, 13}. We show that if this number is greater than 10, an unsettled open problem can be solved that three orthonormal bases can not distinguish all pure states in H4. For any dimension d, we construct d + 2k − 2 adaptive rank-1 positive operators for the reconstruction of any unknown pure state in H d , where 1 ≤ k ≤ d.

Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and technology, can be used to determine unknown quantum states completely. In this study, methods to determine multi‐qubit pure quantum states uniquely and directly are explored. Two adaptive protocols are proposed, with their respective quantum circuits. Herein, two or three observables are sufficient, while the number of measurement outcomes are either the same as or fewer than those in existing methods. Additionally, experiments on the IBM 5‐qubit quantum computer, as well as numerical investigations, demonstrate the feasibility of the proposed protocols.

In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {|0 0|, |1 1|}. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases {B 1 , B 2 , B 3 }. Denote the unitary transition matrices from B 1 to {B 2 , B 3 } as U 1 and U 2 . All 32 elements of matrices U 1 and U 2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.