Quantum Data Hiding

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 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.Comment: 19 pages, IEEE style, 8 figures, submitted to IEEE Transactions on Information Theor

Quantum data hiding with spontaneous parameter down-conversion

Here we analyze the practical implication of the existing quantum data hiding protocol with Bell states produced with optical downconverter. We show that the uncertainty for the producing of the Bell states with spontaneous parameter down-conversion should be taken into account, because it will cause serious trouble to the hider encoding procedure. A set of extended Bell states and a generalized Bell states analyzer are proposed to describe and analyze the possible states of two photons distributing in two paths. Then we present a method to integrate the above uncertainty of Bell states preparation into the dating hiding procedure, when we encode the secret with the set of extended Bell states. These modifications greatly simplify the hider's encoding operations, and thus paves the way for the implementation of quantum data hiding with present-day quantum optics.Comment: 4 pages, 1 figure, adding some analyse for security proof, to be appear in Phys. Rev.

Quantum data hiding in the presence of noise

When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can decode reliably if they bring their systems together and perform a collective measurement. This phenomenon is known as quantum data hiding and hitherto has been studied under the assumption that noise does not affect the encoded systems. With the aim of applying the quantum data hiding effect in practical scenarios, here we define the data-hiding capacity for hiding classical information using a quantum channel. Using this notion, we establish a regularized upper bound on the data hiding capacity of any quantum broadcast channel, and we prove that coherent-state encodings have a strong limitation on their data hiding rates. We then prove a lower bound on the data hiding capacity of channels that map the maximally mixed state to the maximally mixed state (we call these channels "mictodiactic"---they can be seen as a generalization of unital channels when the input and output spaces are not necessarily isomorphic) and argue how to extend this bound to generic channels and to more than two receivers.Comment: 12 pages, accepted for publication in IEEE Transactions on Information Theor

Private states, quantum data hiding and the swapping of perfect secrecy

We derive a formal connection between quantum data hiding and quantum privacy, confirming the intuition behind the construction of bound entangled states from which secret bits can be extracted. We present three main results. First, we show how to simplify the class of private states and related states via reversible local operation and one-way communication. Second, we obtain a bound on the one-way distillable entanglement of private states in terms of restricted relative entropy measures, which is tight in many cases and shows that protocols for one-way distillation of key out of states with low distillable entanglement lead to the distillation of data hiding states. Third, we consider the problem of extending the distance of quantum key distribution with help of intermediate stations. In analogy to the quantum repeater, this paradigm has been called the quantum key repeater. We show that when extending private states with one-way communication, the resulting rate is bounded by the one-way distillable entanglement. In order to swap perfect secrecy it is thus essentially optimal to use entanglement swapping.Comment: v3 published version, some details of the main proofs have been moved to the appendix, 21 pages. v2 claims changed from LOCC to one-way LOCC in the process of correcting a mistake found in v1 (in proof of Lemma 3). v1: 15 pages, 9 figure

Nonlocal quantum state ensembles and quantum data hiding

We consider the discrimination of bipartite quantum states and establish a relation between nonlocal quantum state ensemble and quantum data hiding processing. Using a bound on optimal local discrimination of bipartite quantum states, we provide a sufficient condition for a bipartite quantum state ensemble to be used to construct a quantum data-hiding scheme. Our results are illustrated by examples in multidimensional bipartite quantum systems.Comment: 11 pages, 4 figure

Quantumness of correlations, quantumness of ensembles and quantum data hiding

We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is

Quantum nonlocality in the presence of superselection rules and data hiding protocols

We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum-nonlocality has to be redefined in the presence of superselection rules: there exist separable states that cannot be prepared locally and exhibit some form of nonlocality. Moreover, the notion of local distinguishability in the presence of classical communication has to be altered. This can be used to perform quantum information tasks that are otherwise impossible. In particular, this leads to the introduction of perfect quantum data hiding protocols, for which quantum communication (eventually in the form of a separable but nonlocal state) is needed to unlock the secret.Comment: 4 page

Local Indistinguishability and Possibility of Hiding cbits in Activable Bound Entangled States

In this letter we prove local indistinguishability of four orthogonal activable bound entangled states shared among even number of parties. All reduced density matrices of such states are maximally mixed. We further proceed to establish a multipartite quantum data hiding scheme on those states and explore its power and limitations.Comment: 10 pages, no figure, latex, final versio