Deterministic tripartite sharing of an arbitrary single-qubit operation with the five-qubit cluster state in a given entanglement structure

Recently Muralidharan and Panigrahi (Phys. Rev. A 78, 062333 2008) had shown that using a five-qubit cluster state as quantum channel, it is possible to teleport an arbitrary single-qubit state and an arbitrary two-qubit state. In this paper, we investigate this channel for the teleportation of a special form of three-qubit state.

A scheme for probabilistic teleportation of an unknown three-atom entangled state via a five-atom non-maximally entangled cluster state as quantum channel is proposed. In this scheme, the sender performs two Bell state and a single-atom measurements on the atoms, the receiver can reconstruct the original state with a certain probability by introducing an auxiliary atom and operating appropriate unitary transformations and controlled-not (C-not) operations according to the sender Alice's measurement results. As a result, the probability of successful teleportation is determined by the smallest two of the coefficients' absolute values of the cluster state. The considerable advantage of our scheme is that we employ a non-maximally entangled cluster state as quantum channel in the scheme, which can greatly reduce the amount of entanglement resources and need less classical bits. If we employ a maximally entangled cluster state as quantum channel, the probabilistic teleportation scheme becomes usual teleportation, the successful probability being 100%.

An experimentally feasible scheme for teleportation of an unknown two-atom entangled state is proposed. Our scheme uses a cluster state as the quantum channel, where we do not need any joint Bell-state measurement. Moreover the successful probability and fidelity of teleportation can both reach 1.0. The current scheme can be realized within the current experimental technology.

We study the quantum Fisher information (QFI) and, thus, the multipartite entanglement structure of thermal pure states in the context of the eigenstate thermalization hypothesis (ETH). In both the canonical ensemble and the ETH, the quantum Fisher information may be explicitly calculated from the response functions. In the case of the ETH, we find that the expression of the QFI bounds the corresponding canonical expression from above. This implies that although average values and fluctuations of local observables are indistinguishable from their canonical counterpart, the entanglement structure of the state is starkly different; with the difference amplified, e.g., in the proximity of a thermal phase transition. We also provide a state-of-the-art numerical example of a situation where the quantum Fisher information in a quantum many-body system is extensive while the corresponding quantity in the canonical ensemble vanishes. Our findings have direct relevance for the entanglement structure in the asymptotic states of quenched many-body dynamics.

Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the other hand, quantum protocol designers may commit much more faults than classical protocol designers since human intuition is much better adapted to the classical world than the quantum world. To offer formal techniques for modeling and verification of quantum protocols, several quantum extensions of process algebra have been proposed. One of the most serious issues in quantum process algebra is to discover a quantum generalization of the notion of bisimulation, which lies in a central position in process algebra, preserved by parallel composition in the presence of quantum entanglement, which has no counterpart in classical computation. Quite a few versions of bisimulation have been defined for quantum processes in the literature, but in the best case they are only proved to be preserved by parallel composition of purely quantum processes where no classical communications are involved. Many quantum cryptographic protocols, however, employ the LOCC (Local Operations and Classical Communications) scheme, where classical communications must be explicitly specified. So, a notion of bisimulation preserved by parallel composition in the circumstance of both classical and quantum communications is crucial for process algebra approach to verification of quantum cryptographic protocols. In this paper we introduce a novel notion of bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communications are present. We also establish some basic algebraic laws for this bisimulation. In particular, we prove uniqueness of the solutions to recursive equations of quantum processes, which provides a powerful proof technique for verifying complex quantum protocols.

We interpret the traversable wormhole in AdS/CFT in the context of quantum information theory. In particular, we investigate its properties as both a quantum channel and entanglement witness. We define protocols that allow either the bounding of the channel’s entanglement capacity or the determination of aspects of the entanglement structure between the two boundary CFTs. Such protocols and connections allow for the use of quantum channel techniques in the study of gravitational physics and vice versa. More generally, our results suggest a purely quantum information-theoretic criterion for recognizing when the product of two boundary theories has a classical bulk interpretation.

The paper studies unambiguous discrimination of fermionic states through local operations and classical communication (LOCC). In the task of unambiguous discrimination, no error is tolerated but an inconclusive result is allowed. We show that contrary to the quantum case, it is not always possible to distinguish two fermionic states through LOCC unambiguously with the same success probability as if global measurements were allowed. Furthermore, we prove that we can overcome such a limit through an ancillary system made of two fermionic modes, independently of the dimension of the system, prepared in a maximally entangled state: in this case, LOCC protocols achieve the optimal success probability.

We establish a converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a “privacy test” to establish a general meta-converse bound for private communication.

Fusing the ideas of hierarchical quantum state sharing and quantum operation sharing, a novel protocol for quantum communication having substantial applications in the future quantum network is designed and analyzed. Concretely, we put forward a five-party quantum rotation operation sharing scheme with the aid of shared five-qubit cluster state and local operation as well as classical communication. The five features in the presented scheme are exposed, and comparing our scenario with existing schemes, we find that some of these important features are not available in existing protocols. Furthermore, we confirm our scheme security via a detailed analysis and reveal the experimental feasibility of the scheme with the current technologies.

We provide two schemes for tripartite Controlled Teleportation (CT) of an arbitrary two-qubit state by using five- and six-qubit cluster states as the quantum channel. It is found that the five-partite cluster state can be used for CT of an arbitrary two-qubit state with three agents and the six-partite cluster state can be used for symmetric CT scheme. In comparison with the similar scheme using the same quantum channels by Muralidharan and Panigrahi [Phys. Rev. A 78 (2008) 062333] and by Menona et al. [arXiv:/0906.3874v1], not multipartite entanglement measurements, which makes our schemes simpler than the existing schemes.

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4)m−1.

Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we resolve this problem by developing a dynamical framework in which quantum Bell nonlocality emerges as special form of entanglement, and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of quantum processes, which are abstract quantum channels mapping elements between fixed intervals in space and time. Entanglement is then identified as a quantum process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input-output delay time. LOCC pre-processing is a natural set of free operations in this theory, thereby enabling all entangled states to activate some form of Bell nonlocality. In addition, we generalize the CHSH witnesses from the state domain to the domain of entangled quantum measurements, and provide a systematic method to quantify the Bell nonlocality of a bipartite quantum channel.

We agree with the correction of the index made by Chen et al. [previous Comment, Phys. Rev. A 79, 036301 (2009)]. We reconfirm that our protocol can be applied to multipartite quantum channels and nonsymmetric quantum channels and that Rogolin's protocol is only a special case of ours.

We show that the max-Rains information of a quantum channel is an efficiently computable, single-letter strong converse upper bound for transmitting quantum information over quantum channels when assisted by positive-partial-transpose (PPT) preserving channels between every use of the channel. This includes in particular the quantum capacity with local operations and classical communication (LOCC) assistance. For our proof we make use of the amortized entanglement of quantum channels, which is defined as the largest net amount of entanglement that can be generated if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of quantum channels when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and the channel's max-Rains information, found recently in [Wang et al., arXiv:1709.00200].

We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network. In this paper, we propose the quantum 2-pair multicast communication scheme, and extend it to k-pair multicast communication over the extended butterfly network. Firstly, an EPR pair is shared between each adjacent node on the butterfly network, and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes. Secondly, each sender adds auxiliary particles according to the multicast number k, in which the CNOT operations are applied to form the multi-particle entangled state. Finally, combined with network coding and free classical communication, quantum multicast communication based on quantum measurements is completed over the extended butterfly network. Not only the bottleneck problem is solved, but also quantum multicast communication can be completed in our scheme. At the same time, regardless of multicast number k, the maximum capacity of classical channel is 2 bits, and quantum channel is used only once.