Highly Entangled States With Almost No Secrecy

Abstract

In this paper we illuminate the relation between entanglement and secrecy by providing the first example of a quantum state that is highly entangled, but from which, nevertheless, almost no secrecy can be extracted. More precisely, we provide two bounds on the bipartite entanglement of the totally antisymmetric state in dimension d x d. First, we show that the amount of secrecy that can be extracted from the state is low, to be precise it is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that we need a large amount of singlets to create the state: entanglement cost is larger than a constant, independent of d. In order to obtain our results we use representation theory, linear programming and the entanglement measure known as squashed entanglement. Our findings also clarify the relation between the squashed entanglement and the relative entropy of entanglement.

5 pages, short version of arXiv:0910.4151

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Cited by in corpus (16)

• Faithful Squashed Entanglement
• Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
• Limitations on Quantum Key Repeaters
• Relative entropy and squashed entanglement
• Entanglement of the Antisymmetric State
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Distillability and PPT entanglement of low-rank quantum states
• Versatile relative entropy bounds for quantum networks
• Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
• Weak multiplicativity for random quantum channels
• Maximal Privacy Without Coherence
• Entangled inputs cannot make imperfect quantum channels perfect
• Computing Multiplicities of Lie Group Representations
• Optimized Correlation Measures in Holography
• Percolation of secret correlations in a network
• Some aspects of the interplay between bipartite correlations and quantum channels