Abstract
The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.
Highlights
The notion of steering was first introduced by Schrödinger in 1935 in order to capture the essence of the Einstein–Podolsky–Rosen argument [1]
A specific criterion is given for the case where f k is replaced by the Shannon entropy, and the bound in Equation (55) is related to entropic uncertainty relation (EUR)
Note here that we define tripartite steering from Alice to Bob and Charlie from the local hidden state (LHS) model given in Equation (2), and in this case we should consider the EUR bounds for separable states, see for example Equations (25), (26), (28), (33) and (34), for the case of qubits and Pauli measurements
Summary
The notion of steering was first introduced by Schrödinger in 1935 in order to capture the essence of the Einstein–Podolsky–Rosen argument [1]. It has been shown that steering plays a fundamental role in various quantum protocols and in entanglement theory In the former, steering characterizes systems useful for one-sided device-independent quantum key distribution [3], subchannel discrimination [4] and randomness generation [5]. Though, that SDP methods can be used to set bounds for steering even in a scenario with a continuum of measurements [22,23,24] Another way of detecting steering is through criteria based on correlations [2,25,26,27,28,29].
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