International Journal of Quantum Information

We study quantum states for which the PPT criterion is both sufficient and necessary for separability. We present a class of 3 × 3 bipartite mixed states and show that these states are separable if and only if they are PPT.

The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The space–time position operator acts in the Hilbert space of functions of space and time. Dynamics, however, makes eigenstates of the time operator unphysical. This poses a problem for the standard interpretation of QM and reinforces the role of alternative interpretations such as the Bohmian one. The Bohmian interpretation, despite of being nonlocal in accordance with the Bell theorem, is shown to be relativistic covariant.

We show that the Bell inequalities lead to a new type of linear-optical Deutsch algorithms. We have considered the use of entangled photon pairs to determine probabilistically two unknown functions. The usual Deutsch algorithm determines one unknown function and exhibits a two to one speed up in a certain computation on a quantum computer rather than on a classical computer. We found that the violation of Bell locality in the Hilbert space formalism of quantum theory predicts that the proposed probabilistic Deutsch algorithm for computing two unknown functions exhibits at least a to one speed up.

In this paper, by using permutation matrices as a representation of symmetric group S_N and Fourier matrix, we investigate quantum roulette with an arbitrary N-state. This strategy, which we introduce, is a general method that allows us to solve quantum game for an arbitrary N-state. We consider the interaction between the system and its environment and study the effect of the depolarizing channel on this strategy. Finally, as an example, we employ this strategy for quantum roulette with N = 3.

We propose a scheme to realize the optimal 1 → 2 universal quantum cloning (UQC) in 2-dimension with superconducting quantum-interference device (SQUID) qubits in a microwave cavity. In our scheme, three-SQUIDs are fixed in a microwave cavity via a Raman transition for their manipulation. Using this method, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the cavity decay is suppressed during the cloning process. Furthermore, our scheme only requires using the two lower flux states of the SQUID system and the excited state is not excited. So the effect of decoherence based on the levels of the SQUID system is possible to minimize.

Deutsch algorithm or Deutsch–Jozsa algorithm only needs one query to determine whether the function f(x) is constant or balanced. That is, the global property of the function f(x) is rapidly known. But these algorithms do not give the concrete value of function f(x). For the f(x), its value is also of interest. Here we propose a scheme in which the value of function f(x) can be determined. We use an entangled state as the input state and send it into quantum black box. Through performing measurement on the output state, we can exactly determine the value of f(x). Its value plus its global property enables us to thoroughly understand elementary information of f(x). Based on these informations, we can determine unitary transformations on the input state walking through quantum black box. The quantum black box becomes quantum white box to a certain extent.

Using quantum dense coding, a quantum secure direct communication scheme with a six-qubit maximally entangled state is proposed. If the first security test is passed, the sender performs unitary transformations to encode the secret information on her particles and sends to the receiver. The receiver then performs projective measurements to decode the secret information. It enables the sender to transmit six-bit classical secret message by sending three particles to the receiver. The second security test is adopted to guarantee the security of the communication.

In this paper, we proposed a protocol which can produce a perfect copy of an unknown three-particle three-dimension equatorial entangled state with assistance from a state preparer. Two stages were included in this protocol. The first stage requires usual teleportation, after Alice's (the state sender) generalized Bell-state measurement. Bob (the state receiver) can get the original state with a certain probability. In the second stage, after having received Victor's (the state preparer) classical message, and using the rest resource of the teleportation process, the perfect copy of an original unknown state can be produced in Alice's place. Furthermore, we have also investigated that the quantum channel is a non-maximally entangled state case. Alice also can re-establish the original unknown state in the certain probability.

We study the relation between energy and entanglement in a multiqubit entanglement dynamics problem in cavity QED. The model consists of three two-level atoms A, B and C which are initially prepared in a Greenberger–Horne–Zeilinger-like state and locally coupled with independent cavities a, b and c, respectively. We shall show that the dynamical evolution of atomic entanglement is closely related to that of their energy.

A scheme for realizing the non-local Toffoli gate among three spatially separated nodes through cavity quantum electrodynamics (C-QED) is presented. The scheme can obtain high fidelity in the current C-QED system. With entangled qubits as quantum channels, the operation is resistive to actual environment noise.

We present a proposal of the quantum secret encryption, transmission, and decryption implementation for quantum secret-sharing protocol using cavity QED. In the proposed scheme, the information is stored in two identical two-level atoms, and the two-qubit logic transformation is realized through the interaction between atoms and a nonresonant cavity mode. The proposed scheme requires no ancilla states to assist the intermediate atomic transitions and conditional quantum dynamics for quantum phase flip and quantum state diffusion. The encryption and decryption of quantum states are mostly governed by the Hamiltonian of an atom-cavity system. Moreover, secret transmission using quasi-swap gates for entanglement swapping has also been presented. With fewer supplements of external fields, a speed quantum protocol can be realized without universal gates.

A novel efficient scheme for deterministic secure quantum communication with cluster state is proposed. By utilizing Bell-basis- and -basis-measurements, the two legitimate users can directly transmit secret message after exchanging some additional classical information. It has a high capacity as each cluster state can carry two bits of information, and has a high intrinsic efficiency because almost all the instances are useful. Since the present scheme is based on the cluster state which is robust against decoherence, it is easily processed by a one-way quantum computer. Furthermore, this scheme is feasible with present-day technique.

This book provides a concise introduction to quantum mechanics for students versed in mathematics and mechanics. Dr Strocchi imparts a holistic perspective of the quantum landscape by focussing on three concepts: the algebra of observables, basic quantum systems, and stochastic processes. After mastering these concepts, readers are prepared to study specific quantum theories of information, statistical mechanics, and fields.