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Physical Review A

Security of Terhal-DiVincenzo-Leung quantum-data-hiding protocol against inconclusive positive-operator-valued measure

Tomoyuki Morimae

Published May 28, 2013• 3 citations
Publisher

Abstract

In the quantum-data-hiding protocol by Terhal, DiVincenzo, and Leung [Phys. Rev. Lett. 86, 5807 (2001)], Charlie can hide a single bit of information into a quantum many-body state in such a way that Alice and Bob who share the quantum many-body state cannot learn the bit with only the local-operation-and-classical-communication protocol. In this paper, we show the security of the quantum-data-hiding protocol against any inconclusive positive-operator-valued measure.

DOI
10.1103/physreva.87.054302

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In the quantum-data-hiding protocol by Terhal, DiVincenzo, and Leung [Phys. Rev. Lett. 86, 5807 (2001)], Charlie can hide a single bit of information into a quantum many-body state in such a way that Alice and Bob who share the quantum many-body state cannot learn the bit with only the local-operation-and-classical-communication protocol. In this paper, we show the security of the quantum-data-hiding protocol against any inconclusive positive-operator-valued measure.
We present protocols for multiparty data hiding of quantum information that implement all possible threshold access structures. Closely related to secret sharing, data hiding has a more demanding security requirement: that the data remain secure against unrestricted attacks via local operation and classical communication. In the limit of hiding a large amount of data, our protocols achieve an asymptotic rate of one hidden qubit per local physical qubit. That is, each party holds a share that is the same size as the hidden state to leading order, with accuracy and security parameters incurring an overhead that is asymptotically negligible. The data-hiding states have very unusual entanglement properties, which we briefly discuss.
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.
Abstract — We expand on our work on Quantum Data Hiding [1] – hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.
We expand on our work on quantum data hiding - hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell (1964) states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data-hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.
One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.
We present a general technique for hiding a classical bit in multipartite quantum states. The hidden bit, encoded in the choice of one of two possible density operators, cannot be recovered by local operations and classical communication without quantum communication. The scheme remains secure if quantum communication is allowed between certain partners, and can be designed for any choice of quantum communication patterns to be secure, but to allow near perfect recovery for all other patterns. No entanglement is needed since the hiding states can be chosen to be separable. A single ebit of prior entanglement is not sufficient to break the scheme.