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Hiding Quantum Data

David Peter Divincenzo, Patrick M. Hayden, Barbara M. Terhal

Published Jul 25, 2002• 28 citations
OpenAlex

Abstract

Recent work has shown how to use the laws of quantum mechanics to keep classical and quantum bits secret in a number of different circumstances. Among the examples are private quantum channels, quantum secret sharing and quantum data hiding. In this paper we show that a method for keeping two classical bits hidden in any such scenario can be used to construct a method for keeping one quantum bit hidden, and vice--versa. In the realm of quantum data hiding, this allows us to construct bipartite and multipartite hiding schemes for qubits from the previously known constructions for hiding bits. Our method also gives a simple proof that two bits of shared randomness are required to construct a private quantum channel hiding one qubit.

Related papers

Quantum data hiding

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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.

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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.

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David Peter Divincenzo, Debbie Leung, Barbara M. Terhal

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.

•Mar 16, 2001•240 citations

(2,m)-threshold quantum data hiding

Donghoon Ha, Jeong San Kim

We consider multiparty quantum state discrimination and present a multiparty quantum data-hiding scheme for one classical bit to be shared among multiple parties. In the proposed scheme, any pair of parties can collaborate to perfectly recover the hidden bit through a joint measurement, whereas measurements based on local operations and classical communication(LOCC) performed even by all parties reveal only an arbitrarily small amount of information. We further provide bounds on the optimal LOCC discrimination of multiparty quantum states. The proposed scheme can be implemented using only separable states of low-dimensional quantum systems, enhancing its practical feasibility.

quant-pharXiv:2607.08070•Journal of Physics A Mathematical and Theoretical•Jul 10, 2026•0 citations
Recent work has shown how to use the laws of quantum mechanics to keep classical and quantum bits secret in a number of different circumstances. Among the examples are private quantum channels, quantum secret sharing and quantum data hiding. In this paper we show that a method for keeping two classical bits hidden in any such scenario can be used to construct a method for keeping one quantum bit hidden, and vice--versa. In the realm of quantum data hiding, this allows us to construct bipartite and multipartite hiding schemes for qubits from the previously known constructions for hiding bits. Our method also gives a simple proof that two bits of shared randomness are required to construct a private quantum channel hiding one qubit.
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.
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.
Quantum data hiding encodes a hidden classical bit to a pair of quantum states that is difficult to distinguish using a particular set of measurement, denoted as MMM. In this work, we explore quantum data hiding in two contexts involving Gaussian operations or states. First, we consider the set of measurement MMM as Gaussian local quantum operations and classical communication, a new set of operations not previously discussed in the literature for data hiding. We hide one classical bit in the two different mixture of displaced two-mode squeezed states. Second, we consider the set of measurement MMM as general Gaussian measurement and construct the data hiding states using two-mode thermal states. This data hiding scheme is effective in the weak strength limit, providing a new example compared to existing discussions for the set of general Gaussian measurement.
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.
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 consider multiparty quantum state discrimination and present a multiparty quantum data-hiding scheme for one classical bit to be shared among multiple parties. In the proposed scheme, any pair of parties can collaborate to perfectly recover the hidden bit through a joint measurement, whereas measurements based on local operations and classical communication(LOCC) performed even by all parties reveal only an arbitrarily small amount of information. We further provide bounds on the optimal LOCC discrimination of multiparty quantum states. The proposed scheme can be implemented using only separable states of low-dimensional quantum systems, enhancing its practical feasibility.