One-way Einstein-Podolsky-Rosen steering beyond qubits

Abstract

Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest steering only in specific direction, thus called oneway steering. Existing works focused on one-way steering in systems of qubits. Here we propose a family of two-party states that are one-way steerable in systems of d-dimension. In particular, we validate the one-way steerability of the states for d = 3, and demonstrate how one-way steering parameter space manifests in two-qutrit system. A general numerical approach for characterizing higher-dimensional one-way steering is provided. Moreover, we develop a method to characterize one-way steering with the experimental loss taken into account, with which the tradeoff relation between losses and measurement settings in steering test in higher-dimensional system is investigated. Our loss-counted model works for finite-dimensional system with finite measurement settings.

Analysis of Quantum Steering Measures

“…In this case, it is possible for Alice to steer Bob’s state in some nonlocal way. It is important to note that, unlike entanglement and Bell’s nonlocality, quantum steering is an asymmetric quantum feature, and there are states where Alice can steer Bob but not the other way around [ 8 , 9 , 10 , 11 ].…”

“…Unlike Bell’s nonlocality [ 5 ] and entanglement [ 6 ], steering [ 7 ] is fundamentally asymmetrical. It allows, for example, entangled systems that are only steerable from one observer to another, known as one-way steering [ 8 , 9 , 10 , 11 ]. This property makes quantum steering an interesting resource for quantum information processing where some of the parties are considered untrusted, such as quantum key distribution [ 12 , 13 ], randomness generation [ 14 , 15 , 16 ], subchannel discrimination [ 17 ], and quantum teleportation [ 18 ].…”

Ascertaining the influences of auxiliary qubits on the Einstein–Podolsky–Rosen steering and its directions

“…Fortunately, due to the nontrivial application of the asymmetry of EPR steering in one-sided device-independent quantum key distribution, [3] observations of the asymmetry of EPR steering have been gradually implemented in different systems. For instance, optical systems, [29] selfphase-locked optical parametric oscillators, [30] dynamical Casimir arrays, [31] high dimension systems, [32] modulated optomechanical systems, [33] cavity magnonics, [34] macroscopic hybrid systems, [35] and so on. Reservoir systems are an important physical model, and the maximal-steeredcoherence of such systems can be controlled by quantum reservoir engineering.…”

Unlimited One-Way Steering

“…Specifically, there exist entangled states that lead to steering from Bob to Alice, but not the other way around [12]; Bob can convince Alice that the shared state is entangled, while Alice can never convince Bob, even if she would use all possible local measurements. This effect, coined "one-way steering" has attracted considerable attention in recent years, with many examples in low-dimensional (mostly 2-qubit) [12][13][14][15][16][17] and continuous variable Gaussian systems [18,19] as well as experimental demonstrations; see, e.g., Refs. [20][21][22][23].…”