All Entangled States can Demonstrate Nonclassical Teleportation

Complete complementarity relations and their Lorentz invariance

It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single-particle states, a spin-momentum product state can be transformed into an entangled state. However, entanglement is just one of the aspects that completely characterizes a quantum system. The other two are known as the wave-particle duality. Although the entanglement entropy does not remain invariant under Lorentz boosts, and neither do the measures of predictability and coherence, we show here that these three measures taken together, in a complete complementarity relation (CCR), are Lorentz invariant. Peres et al. (Peres et al. 2002 Phys. Rev. Lett. 88 , 230402. ( doi:10.1103/PhysRevLett.88.230402 )) realized that even though it is possible to formally define spin in any Lorentz frame, there is no relationship between the observable expectation values in different Lorentz frames. Analogously, one can, in principle, define complementary relations in any Lorentz frame, but there is no obvious transformation law relating complementary relations in different frames. However, our result shows that the CCRs have the same value in any Lorentz frame, i.e. there is a transformation law connecting the CCRs. In addition, we explore relativistic scenarios for single and two-particle states, which helps in understanding the exchange of different aspects of a quantum system under Lorentz boosts.

Experimental High-Dimensional Quantum Teleportation

Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-dimensional Bell state measurement. The fidelity of teleportation process matrix is F=0.596±0.037. Through this process matrix, we can prove that our teleportation is both nonclassical and genuine three dimensional. Our work paves the way to rebuild complex quantum systems remotely and to construct complex quantum networks.

Type-Independent Characterization of Spacelike Separated Resources

Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of spacelike separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present Letter, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.

Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas

In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject dealing with different but connected facets of quantum non-locality, we consider if this, and the friction it carries with special relativity, can eventually find a “solution” by considering higher dimensional spaces.

Improving the Robustness of Entangled States by Basis Transformation

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

Experimental Study of Nonclassical Teleportation Beyond Average Fidelity

Quantum teleportation establishes a correspondence between an entangled state shared by two separate parties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was recently shown that if one considers a finer-grained witness, then all entangled states can be certified to produce a nonclassical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110501 under different conditions of noise. We report nonclassical teleportation using quantum states that cannot achieve average fidelity of teleportation above the classical limit. We further use the violation of these witnesses to estimate the negativity of the shared state. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.

Two-copy Quantum Teleportation

We investigate two-copy scenario of quantum teleportation based on Bell measurements. The detailed protocol is presented and the general expression of the corresponding optimal teleportation fidelity is derived, which is given by the two-copy fully entangled fraction that is invariant under local unitary transformations. We prove that under a specific case of the protocol, which is significant for improving the optimal fidelity, the set of states with their two-copy fully entangled fractions bounded by a threshold value that required for useful two-copy teleportation is convex and compact. Hence the witness operators exist to separate states that are useful for two-copy teleportation from the rest ones. Moreover, we show that the optimal fidelity of two-copy teleportation surpasses that of the original one copy teleportation.