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arXiv:1402.4235 · Physical Review A

Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities

M. D. Reid

Published Dec 30, 2013• 157 citations
arXivHTMLPDF

Abstract

The demonstration of quantum teleportation of a photonic qubit from Alice to Bob usually relies on data conditioned on detection at Bob's location. I show that Bohm's Einstein-Podolsky-Rosen (EPR) paradox can be used to verify that the quantum benchmark for qubit teleportation has been reached, without postselection. This is possible for scenarios insensitive to losses at the generation station, and with efficiencies of ${\ensuremath{\eta}}_{B}>1/3$ for the teleportation process. The benchmark is obtained if it is shown that Bob can ``steer'' Alice's record of the qubit as stored by Charlie. EPR steering inequalities involving $m$ measurement settings can also be used to confirm quantum teleportation, for efficiencies ${\ensuremath{\eta}}_{B}>1/m$, if one assumes trusted detectors for Charlie and Alice. Using proofs of monogamy, I show that two-setting EPR steering inequalities can signify secure teleportation of the qubit state.

DOI
10.1103/physreva.88.062338

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The demonstration of quantum teleportation of a photonic qubit from Alice to Bob usually relies on data conditioned on detection at Bob's location. I show that Bohm's Einstein-Podolsky-Rosen (EPR) paradox can be used to verify that the quantum benchmark for qubit teleportation has been reached, without postselection. This is possible for scenarios insensitive to losses at the generation station, and with efficiencies of \ensuremathηB>1/3{\ensuremath{\eta}}_{B}>1/3\ensuremathηB​>1/3 for the teleportation process. The benchmark is obtained if it is shown that Bob can ``steer'' Alice's record of the qubit as stored by Charlie. EPR steering inequalities involving mmm measurement settings can also be used to confirm quantum teleportation, for efficiencies \ensuremathηB>1/m{\ensuremath{\eta}}_{B}>1/m\ensuremathηB​>1/m, if one assumes trusted detectors for Charlie and Alice. Using proofs of monogamy, I show that two-setting EPR steering inequalities can signify secure teleportation of the qubit state.
Einstein-Podolsky-Rosen (EPR) steering refers to the type of correlations described in the EPR paradox, where one observer seems to affect (”steer”) the state of other observer by using local measurements. There have been several works regarding characterization and quantification of EPR steering. One characteristic of this non-local correlation is that it can be asymmetric, while entanglement is symmetric. This asymmetric property is relevant for potential applications of EPR steering to quantum information, in particular to quantum cryptography and quantum teleportation. This latter refers to the process where one observer sends an unknown quantum state to Bob, who is in a different location. They communicate by classical means. Here we will show that EPR steering is a necessary resource to obtain secure continuous variable teleportation. We will also consider NOON states, which is an example of an entangled state. For this state, we will present a steering signature. This contribution reviews the work derived in Refs. [1] and [2], which was presented as an invited talk in ELAF 2017.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the earliest paradoxes, arising from the lack of local realistic description of mechanics. The EPR paradox leads to the important concept of quantum which manifests itself by three different phenomena: entanglement, steering, and Bell's nonlocality. Two well-known paradoxes related to Bell's nonlocality, i.e. the Greenberger-Horne-Zeilinger paradox and the Hardy paradox, have been widely studied and also experimentally confirmed. However, an experimental test of the EPR paradox is still lacking. The EPR paradox is essentially a steering paradox, and recently it has been mathematically formulated as a contradiction equality k=1k=1k=1, thus making it amenable to an experimental verification. Moreover, based on the EPR paradox we also derive a generalized linear steering inequality. In this work, we perform the first experimental test of the EPR paradox in a two-qubit scenario, and also verify the corresponding generalized steering inequality, which has an advantage over the usual one by detecting more steerability of states. Experimental results confirm the theoretical predictions within the experimental errors, and provide a deeper understanding of foundation.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it amenable to an experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is more friendly for experimental implementation, i.e., one may only measure the observables in xxx-, yyy-, or zzz-axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with the theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.
Abstract Quantum paradoxes are essential means to reveal the incompatibility between quantum and classical theories, among which the Einstein-Podolsky-Rosen (EPR) steering paradox offers a sharper criterion for the contradiction between local-hidden-state model and quantum mechanics than the usual inequality-based method. In this work, we present a generalized EPR steering paradox, which predicts a contradictory equality “2Q=(1+δ)C2_{Q}=\left(1+\delta\right)_{C}2Q​=(1+δ)C​” (0≤δ＜10\leq\delta＜10≤δ＜1) given by the quantum (QQQ) and classical (CCC) theories. For any NNN-qubit state in which the conditional state of the steered party is pure, we test the paradox through a two-setting steering protocol, and find that the state is steerable if some specific measurement requirements are satisfied. Moreover, our construction also enlightens the building of EPR steering inequality, which may contribute to some schemes for typical quantum teleportation and quantum key distributions.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
Abstract Einstein–Podolsky–Rosen (EPR) steering is an important quantum resource in quantum information and computation. The relationships between EPR steering and the fidelity of quantum teleportation for two- and three-qubit states are investigated in this paper. For two-qubit states, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the two-qubit X-type states which violate the three-setting measurements steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of two-qubit reduced states for three-qubit pure states maintain the same ordering. The complementary relations between the steering observables and the average teleportation fidelities for three-qubit pure states are also established.