Scheme for implementing quantum dense coding with four-particle decoherence-free states in an ion trap

In this article I review some results obtained during my PhD work in the group of Professor Messina, at the University of Palermo. I discuss some proposals aimed at exploring fundamental issues of quantum theory, e.g. entanglement and quantum superpositions, in the context of single trapped ions. This physical context turns out to be extremely well suited both for studying fundamental features of quantum mechanics, such as the quantum–classical border, and for technological applications such as quantum logic gates and quantum registers. I focus on some procedures for engineering nonclassical states of the vibrational motion of the centre of mass of the ion. I consider both the case in which the ion interacts with classical laser beams and the case of interaction with a quantized mode of light. In particular, I discuss the generation of Schrodinger cat-like states, Bell states and Greenberger–Horn–Zeilinger states. The schemes for generating nonclassical states stem from two different quantum processes: the parity effect and the quantum state manipulation via quantum non-demolition measurement. Finally, I consider a microscopic theory of the interaction of a quantum harmonic oscillator (the centre of mass of the ion in the trapped ion context) with a bosonic thermal environment. Using an exact approach to the dynamics, I discuss a quantum theory of heating of trapped ions able to describe both the short time non-Markovian regime and the thermalization process. I conclude showing briefly how the trapped ion systems can be used as simulators of key models of open quantum systems such as the Caldeira–Leggett model.

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender’s encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid . In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness. We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of d 2 possible messages by sending a d -dimensional quantum state, for general dimensions d . Unlike the d =2 case (i.e., sending a single qubit), there can be inequivalent superdense coding protocols for higher d . We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all d > 2. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.

Two faithful quantum secure communication and authentication schemes based on Bell states and classical XOR operation are proposed, which withstand collective noises. The authentication and eavesdropping detection are completed by using logical decoy photons generating by previously shared identity string. The logical decoy photons are decoherence-free states over the two collective noisy channels respectively. The transmission of secret message is a one-time pad system, which guarantees the absolute security of secret message. Encoding secret message after particle transmission ensures the accuracy of secret message.

The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this Letter, we implement a simple and precise technique that produces any of the four Bell states in the orbital angular momentum degree of freedom. We then use these states to perform the first experimental demonstration of an accessible nonlinear entanglement witness. Such a witness determines entanglement by using the same measurements as required for a linear witness but can detect, in this case, twice as many states as a single linear witness can. We anticipate that our method of state preparation and nonlinear witnesses will have further uses in areas of quantum science, such as superdense coding and quantum key distribution.

Super dense coding is a well known protocol to communicate two classical bits using a pre-shared pair of entangled qubits. We consider the case of quantum communication over the noisy bit flip channel with a shared Bell pair and show that the encoding scheme is perfectly secure. We extend the idea of super dense coding to a tripartite system and derive expressions for Holevo capacity and accessible information for various communication scenarios among the node links.

We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.

We present a scheme for probabilistic dense coding via quantum channels of non-maximally entangled three-particle states. Quantum dense coding will succeed with a certain probability if the sender introduces an auxiliary particle and performs a collective unitary transformation. The average information transmitted in this scheme is calculated.

Pulse-based Electron–Nuclear and ELectron–electron DOuble Resonance (ENDOR/ELDOR) techniques have been applied to molecular spins in order to implement ensemble electron spin-qubit based quantum computers/computing (QC) and quantum information processing (QIP) in the solid state. Pulsed ENDOR-based QC/QIP experiments for super dense coding (SDC) have for the first time been carried out by the use of molecular electron- and nuclear-spin entities such as the stable malonyl radical as matter spin-qubits. The spin-qubit manipulation technology for quantum gate operations in this work is based on the time-proportional-phase-increment (TPPI) technique, enabling us to distinguish between the phases of spin-qubit based entangled states. The TPPI technique, as firstly applied by Mehring et al. (M. Mehring, J. Mende and W. Scherer, Phys. Rev. Lett., 2003, 90, 153001), has illustrated the establishment of quantum entanglement between electron- and nuclear-spin states and mutual interconversion between the electron–nuclear Bell states. The electron-spin 4π-periodicity in phase shows up in the QC/QIP experiments, explicitly and experimentally illustrating the electron-spin spinor nature for the first time. Tripartite QC experiments have been made, showing the occurrence of separable states. Also, the development of novel electron-spin technology to manipulate multi-electron spin-qubits is described. In this work, the pulsed coherent-dual ELDOR for QC/QIP has for the first time been implemented by invoking a novel microwave dual phase-rotation technique. Thus, applications of the coherent-dual ELDOR to molecular electron spin-qubit systems are also discussed, emphasising designing the molecular two electron-qubit systems appropriate for QC/QIP. g- and/or hyperfine A-tensor engineering approaches give us the two- and multi-electron-qubit systems, which have been a materials challenge to implement matter spin-qubit based QC/QIP. The targeted matter spin-qubits can be used to facilitate selective resonant microwave excitations achieved by the pulsed ELDOR technique. In addition to DiVincenzo's five criteria, general requisites for scalable electron spin-qubit systems as 1D periodic robust spin structures are described. According to the requisites, double- or triple-stranded helicates embedding open-shell metal cations are proposed instead of organic molecular spin-qubits.

Utilizing the notation in Refs. 10 and 11, we revisit general bipartite Bell state for any (d × d) dimensional systems. In particular, we bring out the conditions for general bipartite Bell state and find out the relation between general Bell states and the u(d) group. Furthermore, we construct local unitary complete set for quantum dense coding based on general Bell states.

In Ref. 1 , we proposed a multiparty quantum secret sharing QSS protocol based on Bell-state entanglement swapping. Our multiparty protocol is a general one, that is, it contains both the three-party n=3 case and its generalization to a more-party n 4 case. Recently, in Ref. 2 the authors first pointed out some advantages of our protocol, such as dense coding, easy implementation, high efficiency, etc. Then they claimed that if our protocol is attacked by the so-called participant attack, the protocol is insecure. In fact, our multiparty n 3 QSS protocol is secure against any outsiders’ or insider’s eavesdropping. Only the generalized protocol i.e., the n 4 QSS protocol is insecure under the specific dishonest insiders’ attack as shown in Ref. 2 . Nonetheless, this leak in the generalized protocol can be easily fixed and accordingly the advantage of high efficiency in our protocol can be retained. We will explain these as follows. In Ref. 1 , when we simply generalized our three-party protocol to a n n 4 -party one, we changed the original qubit distribution method due to our carelessness. The original distribution method is that Alice prepares the qubits and distributes them to her two agents. When generalizing, we changed the qubit distribution in such a way that each party sends a qubit to the next party. It is this change which leads to the insecurity under the special attack case 2 . The comment 2 aims essentially at this change. That is, the two dishonest parties who each initially shares an e-bit with the sender can let one of them share both the two e-bits and the other one shares none by exchanging their qubits and cheating. In this case, the protocol is insecure. It is a minor leak in our protocol. If the change about qubit distribution is removed during the generalization, that is, the same qubit distributions as that in the three-party case are maintained when generalizing, then the security of the n n 4 -party protocol can still be assured. The reason is as follows. When the sender distributes two qubits to an agent one by one, if the sender does not tell the agent the orderings of the two qubits, the agent cannot distinguish their orderings for the two qubits are identical. In this case, the two agents who share entanglements with the sender cannot assure that only one of them can definitively share the entanglements with the sender by exchanging their qubits. To be explicit, let us take the four-party case as an example: Alice prepares four photon Einstein-Podolsky-Rosen EPR pairs A2,B1 , B2,C1 , C2,D1 , and D2,A1 . She sends two photons B1,B2 to Bob, C1,C2 to Charlie, and D1, D2 to Dick. In this case, Alice shares the EPR pair A2, B1 with Bob and the EPR pair A1, D2 with Dick. Note that each sharer Bob, Charlie, Dick cannot differentiate his two photons since their two photons are identical. In this case, Bob or Dick cannot correctly let only one sharer say, Bob hereafter share two EPR pairs by exchanging their photons. Obviously, with probability 1/2 Bob may send the photon B1 to Dick. Also with probability 1/2, Dick may send the photon D1 to Bob. In either case, the goal of deterministically letting Bob share two EPR pairs with Alice cannot be realized via the exchange. Consequently, the so-called participant attack is invalid. Hence the leak in our generalized protocol can be easily fixed and accordingly the advantage of high efficiency the authors of Ref. 2 admitted is retained. Incidentally, the modification in Ref. 2 can fix the leak of our protocol also, however, it decreases the efficiency of the protocol.

A two-receiver quantum dense coding scheme and an $N$-receiver quantum dense coding scheme, in the case of non-symmetric Hilbert spaces of the particles of the quantum channel, are investigated in this paper. A sender can send his messages to many receivers simultaneously. The scheme can be applied to quantum secret sharing and controlled quantum dense coding.

Quantum entanglement is the most representative feature of quantum mechanics to classical mechanics. It is the delocalization, non-classical strong correlation among multiple quantum system. It has been developed for nearly one hundred years and a lot of methods of production and applications have been proposed. Aiming at the generation mode of quantum entanglement, this study presents two general preparation methods of quantum entanglement sources, including spontaneous parametric down-conversion (SPDC) and the preparation of quantum entanglement sources based on the four-wave mixing (FWM) effect. The principle, advantages and disadvantages of quantum entanglement sources are analyzed respectively. Finally, the research and application direction of the preparation method of quantum entanglement source are prospected. With the ability of preparation of quantum entanglement source, the application of quantum entanglement developed quickly, (e.g., quantum teleportation, entanglement swapping, quantum key distribution and quantum dense coding in the area of communication), and other area such as quantum computer, quantum imaging, quantum ranging and quantum clock synchronization. These results shed light on guiding further exploration of entanglement fabrication.

Quantum dense coding is considered to be one of the most remarkable demonstrations of the existence of quantum entanglement. In this paper, we analyze the role of correlations (both classical and quantum) in quantum communication protocols. We study how the capacity of a single-qubit quantum channel depends on correlations between Alice and Bob. In particular, we consider a scenario when Alice and Bob share a pair of qubits in a state such that Alice's qubit is in the state described by the density operator $\ensuremath{\varrho}=\frac{1}{2}1+\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}.$ We evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice, and (2) in the case when he utilizes correlations that have been established prior to the communication. We present a simple classical scenario which might serve as a prototype of quantum dense coding. We generalize our results also for qudits. In addition, we address some aspects of the issue of security in correlation-assisted communication protocols.

Dynamics of coded information over Bloch channels is investigated. We show that the coded information is sent with high accuracy over the Bloch channel by increasing the absolute equilibrium value of the information carrier or decreasing the ratio of relaxation time. The robustness of coded information in maximum and partial entangled states is discussed. It is shown that, the maximum entangled states are more robust than the partial entangled state over these types of channels. The dynamics of the local and the non-local information is investigated for different values of the channel's parameters and the initial state setting. It is found that by increasing the absolute equilibrium values for both qubits, the local information of both qubits decreases faster and consequently the information gained by the eavesdropper increases.