We consider the simulation of a quantum channel by two parties who share a resource state and may apply local operations assisted by classical communication (LOCC). One specific type of such LOCC is standard teleportation, which is however limited to the simulation of Pauli channels. Here we show how we can easily enlarge this class by means of a minimal perturbation of the teleportation protocol, where we introduce noise in the classical communication channel between the remote parties. By adopting this noisy protocol, we provide a necessary condition for simulating a non-Pauli channel. In particular, we characterize the set of channels that are generated assuming the Choi matrix of an amplitude damping channel as a resource state. Within this set, we identify a class of Pauli-damping channels for which we bound the two-way quantum and private capacities.
We consider the simulation of a quantum channel by two parties who share a resource state and may apply local operations assisted by classical communication (LOCC). One specific type of such LOCC is standard teleportation, which is however limited to the simulation of Pauli channels. Here we show how we can easily enlarge this class by means of a minimal perturbation of the teleportation protocol, where we introduce noise in the classical communication channel between the remote parties. By adopting this noisy protocol, we provide a necessary condition for simulating a non-Pauli channel. In particular, we characterize the set of channels that are generated assuming the Choi matrix of an amplitude damping channel as a resource state. Within this set, we identify a class of Pauli-damping channels for which we bound the two-way quantum and private capacities.
We begin this thesis by expanding the technique of teleportation simulation, which adds noise to the entangled resource state to mimic channel effects. By introducing classical noise in the communication step, we show it is possible to simulate more than just Pauli channels using teleportation. This new class is characterised, and studied in detail for a particular resource state, leading to a family of simulable channels named "Pauli-Damping channels" whose properties are analysed. Also introduced are a new family of quantum states, "phase Werner" states, whose entanglement properties relate to the interesting conjecture of bound entangled states with a negative partial transpose. Holevo-Werner channels, to which these states are connected, are shown to be teleportation covariant. We exploit this to present several interesting results, including the optimal estimation of the channel-defining parameter. The minimal binary-discrimination error for Holevo-Werner channels is bounded for the first time with the analytical form of the quantum Chernoff bound. We also consider the secret key capacity of these channels, showing how different entanglement measures provide a better upper bound for different regions of these channels. Finally, a method for generating new Bell inequalities is presented, exploiting nonphysical probability distributions to obtain new inequalities. Tens of thousands of new inequivalent inequalities are generated, and their usefulness in closing the detection loophole for imperfect detectors is examined, with comparison to the current optimal construction. Two candidate Bell inequalities which may equal or beat the best construction are presented.
In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.
Quantum teleportation in the presence of noisy channels acting on a bipartite resource state is considered. We consider a family of generalized noisy channels that continuously connect the amplitude damping and the dephasing channels, encompassing a wide family of in-between scenarios, to delve into the relation between the teleportation success and the amount of three- and four-partite entanglement (distributed among the qubits of the resource state and those representing local environments) generated during the evolution. Our analysis reveals that for a fixed entanglement of the resource state, the channels that better protect the teleportation fidelity against the detrimental effects of noise are those that generate higher amounts of (Greenberger-Horne-Zeilinger--type) multipartite entanglement. This suggests that the dynamically induced multipartite correlations may serve as an additional resource for teleportation and provides insight into the characterization of processes and of the type of induced entanglement according to their ability to assist the protocol.
Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). In this paper, we develop two seemingly different ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for several key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example consists of a resource state resulting from the action of a generalized amplitude damping channel on two Bell states, for which we find an analytical expression for the simulation error that is in agreement with numerical estimates (up to numerical precision). We then evaluate the performance of some schemes for bidirectional teleportation due to (Kiktenko et al., Phys. Rev. A 93, 062305 (2016)) and find that they are suboptimal and do not go beyond the aforementioned classical limit for bidirectional teleportation. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information, and we establish semi-definite programming lower bounds on the simulation error for this task. More generally, we provide semi-definite programming lower bounds on the performance of bipartite and multipartite channel simulation using a shared resource state and LOCC.
We quantify in a unified approach the nonlocal resources of bipartite quantum channels and identify their component resisting the effects of dephasing noise. Despite its classical nature, we demonstrate that the latter plays a relevant role in performing quantum protocols, such as state transformations and quantum coding for noisy communication. When comparing different resource types, we show that simulating certain stochastic processes with quantum channels has a communication advantage with respect to their classical simulation, even when dephasing noise occurs. This approach also allows us to lower bound the amount of shared entanglement and communication needed to simulate bipartite quantum channels and to inner approximate the set of n-round local operations, assisted with classical communication.
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. Specifically, two individuals make use of a shared resource state as well as local operations and classical communication (LOCC) to swap quantum states. In this work, we concisely highlight the contributions of our companion paper [A. U. Siddiqui and M. M. Wilde, arXiv:2010.07905 (2020)]. We develop two different ways of quantifying the error of nonideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity. We then establish that the values given by both metrics are equal for this task. Additionally, by relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semidefinite programing lower bounds on the error of nonideal bidirectional teleportation. We evaluate these bounds for some key examples—isotropic states and when there is no resource state at all. In both cases, we find an analytical solution. The second example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example that we investigate consists of two Bell states that have been sent through a generalized amplitude damping channel. For this scenario, we find an analytical expression for the error, as well as a numerical solution that agrees with the former up to numerical precision.