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arXiv:2502.00670

Gaussian quantum data hiding

Yunkai Wang, Smith, Graeme

Published Feb 2, 2025• 0 citations
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Abstract

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 $M$. In this work, we explore quantum data hiding in two contexts involving Gaussian operations or states. First, we consider the set of measurement $M$ 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 $M$ 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.

DOI
10.48550/arxiv.2502.00670

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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.
Suppose we want to benchmark a quantum device held by a remote party, e.g., by testing its ability to carry out challenging quantum measurements outside of a free set of measurements M\mathcal{M}M. A very simple way to do so is to set up a binary-state discrimination task that cannot be solved efficiently by means of free measurements. If we can find pairs of orthogonal states that become arbitrarily indistinguishable under measurements in M\mathcal{M}M, in the sense that the error probability in discrimination approaches that of a random guess, we say that there are data hiding against M\mathcal{M}M. Here we investigate data hiding in the context of continuous-variable quantum systems. First, we look at the case where M\mathcal{M}M denotes the set of measurements implementable with local operations and classical communication. While previous studies have placed upper bounds on the maximum efficiency of data hiding in terms of the local dimension and are thus not applicable to continuous-variable systems, we establish more general bounds that rely solely on the local mean photon number of the states employed. Along the way, we perform a rigorous quantitative analysis of the error introduced by the nonideal Braunstein-Kimble quantum teleportation protocol, determining how much squeezing and local detection efficiency are needed in order to teleport an arbitrary multimode local state of known mean energy with a prescribed accuracy. Finally, following a seminal proposal by Sabapathy and Winter, we look at data hiding against Gaussian operations assisted by the feedforward of measurement outcomes, providing an example of a relatively simple scheme that works with a single mode only.
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.
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.
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 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.