Quantum data hiding

By David P. DiVincenzo, Debbie W. Leung, Barbara M. Terhal. IEEE Transactions on Information Theory, 2001

476 citations recorded by the source corpus.

We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in n, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/843d2278b9964a1d5936b4fe3a9e21d9fa9098b3

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Citations in the corpus

Random Quantum Circuits are Approximate 2-designs (2008, methodology): “Approximate unitary 2-designs have been considered [13, 10, 17], although the approaches are specific to 2-designs.”
Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “On the single gate level, the random Clifford unitaries approximate the random Haar unitaries quite well, being known as a unitary 2-design [31].”
Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “Although these special properties of stabilizer circuits make many aspects of their dynamics nongeneric, one of the defining features of the Clifford group is that it forms a unitary t-design for t ≤ 3 [56, 57].”
Exponential Decay of Correlations Implies Area Law (2012, background): “Quantum states with this property are termed quantum data hiding states, due to their use in hiding correlations (and information) from local measurements [28].”
Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, background): “If A ( t ) ( X ) = 0 for all operators X , then averaging over elements of U agrees with averaging over elements of the Haar distribution over U ( d ) up to the t -th moment, and thus U forms a t -design [54–58].”
Randomizing Quantum States: Constructions and Applications (2003, background): “This basic insight provides the intuition behind a new scheme for data hiding in a bipartite system [5, 6, 7].”
Operator Spreading in Random Unitary Circuits (2017, background): “This is a consequence of the fact that the Clifford group is a unitary 2-design [79].”
The mother of all protocols: restructuring quantum information’s family tree (2006, background): “In fact, DiVincenzo, Leung and Terhal have shown that where G n is the Clifford group on n qubits [29].”
Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask) (2012, background): “is PPT. In terms of Kraus representations, we can equivalently say that a CP map E is separable (PPT) if it admits a Kraus decomposition E(·) = ∑t i=1 M (·)M † such that M†M is a tensor-product (PPT) [DLT02]. Operationally, these classes are more powerful than LOCC, yet they are still more 6 restric”
Measuring entanglement entropy in a quantum many-body system (2015, background): “In some cases, such as in the ‘data hiding states’ [52], mutual information is more appropriate than the more conventional two point correlators which might take arbitrarily small values in presence of strong correlations.”