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.
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. O…
We provide a non-interactive quantum bit commitment scheme which has statistically-hiding and computationally-binding properties from any quantum one-way function. Our protocol is basically a parallel composition of the previous non-interactive quantum bit commitment schemes (based on quantum one-way permutations, due to Dumais, Mayers and Salvail (EUROCRYPT 2000)) with pairwise independent hash functions. To construct our non-interactive quantum bit commitment scheme from any quantum one-way function, we follow the procedure below: (i) from Dumais-Mayers-Salvail scheme to a weakly-hiding and …
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 LOCC attacks. 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 negligib…
Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this fundamental test has not been explored in any of the experimental architecture. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan [New J. Phys. 13, 043016 (2011)] has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. T…
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 hid…
The information bleaching refers to any physical process that removes quantum information from the initial state of the physical system. The no-hiding theorem proves that if information is lost from the initial system, then it cannot remain in the bipartite quantum correlation and must be found in the remainder of the Hilbert space. We show that when hiding map acts on the input state in the presence of indefinite causal order, then it is possible to hide quantum information in the correlation. One may ask, does it then violate the no-hiding theorem? We analyse this question and argue that in …
A method to hide certain quantum states in a superposition will be proposed. Such method can be used to increase the security of a communication channel. States represent an encrypted message will disappear during data exchange. This makes the message 100% safe under direct measurement by an eavesdropper. No entanglement sharing is required among the communicating parties.
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 prepar…
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. The maximal probability of unwanted recovery of the hidden bit, as well as the maximal error for allo…
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 cor…
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 introductio…
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 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…
We present and analyze a protocol for quantum steganography where the sender (Alice) encodes her steganographic information into the error syndromes of the perfect (five-qubit) quantum error-correcting code, and sends it to the receiver (Bob) over a depolarizing channel. Alice and Bob share a classical secret key, and hide quantum information in such a way that to an eavesdropper (Eve) without access to the secret key, the quantum message looks like an innocent codeword with a typical sequence of quantum errors. We calculate the average rate of key consumption, and show how the protocol improv…
Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
Central High School（中央高中）；Department of Mathematics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校数学系）；Department of Physics, University of Rhode Island（罗德岛大学物理系）
The absence of information -- entirely or partly -- is called ignorance. Naturally, one might ask if some ignorance of a whole system will imply some ignorance of its parts. Our classical intuition tells us yes, however quantum theory tells us no: it is possible to encode information in a quantum system so that despite some ignorance of the whole, it is impossible to identify the unknown part arXiv:1011.6448. Experimentally verifying this counter-intuitive fact requires controlling and measuring quantum systems of high dimension $(d {>} 9)$. We provide this experimental evidence using the tran…
Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity and the unitarity. Together with the stronger no-cloning theorem they provide permanence to quantum information, thus, suggesting that in the quantum world information can neither be created nor be destroyed. In this sense quantum information is robust, but at the same time it is also fragile because any interaction with the environment may lead to loss of in…
In this work spontaneous (non-dynamical) breaking (effective hiding) of the unitary quantum mechanical dynamical symmetry (superposition) is considered. It represents an especial but very interesting case of the general formalism of the spontaneous symmetry breaking (effective hiding). Conceptual analogies with spontaneous breaking of the gauge symmetry in Weinberg-Sallam's electro-weak interaction are pointed out. Also, consequences of the spontaneous superposition breaking in the measurement process are discussed. Measurement can be considered as a typical Landau's continuous phase transitio…
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…
Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all quantum information according to the no-hiding and no-masking theorems derived recently. Here we show that any set of informationally complete quantum states is neither hidable nor maskable, thereby strengthening the no-hiding and no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices (representations of the Clifford algebra), we show that information about real quantum states can be completely hidden in the correlations, although t…
We show that the quantum nature of light can be used to hide a secret message within a photograph. Using this physical principle we achieve information-theoretic secure steganography, which had remained elusive until now. The protocol is such that the digital picture in which the secret message is embedded is perfectly undistinguishable from an ordinary photograph. This implies that, on a fundamental level, it is impossible to discriminate a private communication from an exchange of photographs.
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming equal priors). The Holevo-Helstrom theorem says that for the set of all measurements this norm is the trace norm. For finite dimension any norm is lower and upper bounded by constant (though dimension dependent) multiples of the trace norm, so we set ourselves the task of computing or bounding the best possible "constants of domination" for the norms corresp…
We demonstrate an information hiding and retrieval scheme with the relative phases between states in a Rydberg wave packet acting as the bits of a data register. We use a terahertz half-cycle pulse (HCP) to transfer phase-encoded information from an optically accessible angular momentum manifold to another manifold which is not directly accessed by our laser pulses, effectively hiding the information from our optical interferometric measurement techniques. A subsequent HCP acting on these wave packets reintroduces the information back into the optically accessible data register manifold which …
The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. The relevant figure of merit is the maximal ratio (called data hiding ratio) between the distinguishability norms associated with the two sets of measurements we are comparing, typically all measurements vs LOCC protocols. For a bipartite $n\times n$ quantum system, it is known that the data hiding ratio scales as $n$, i.e. the square root of the re…
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 $\mathcal{M}$. 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 one can find pairs of orthogonal states that become arbitrarily indistinguishable under measurements in $\mathcal{M}$, in the sense that the error probability in discrimination approaches that of a random guess, one says that there is data hiding against $\mat…
Quantum state verification (QSV) and quantum data hiding (QDH) have so far been studied separately. QSV decides whether a given quantum state is close to the ideal one, with significantly lower sample complexity compared with direct application of quantum tomography. On the other hand, QDH is a cryptographic protocol that encodes secret classical information in multipartite quantum states, providing stronger security guarantees than conventional classical secret-sharing schemes. Here, we consider two fundamental quantities of a pure quantum state, determining the sample complexity needed for Q…
We show that the positivity of the Wigner function of Gaussian states and measurements provides an elegant way to bound the discriminating power of "linear optics", which we formalise as Gaussian measurement operations augmented by classical (feed-forward) communication (GOCC). This allows us to reproduce and generalise the result of Takeoka and Sasaki [PRA 78:022320, 2008], which tightly characterises the GOCC norm distance of coherent states, separating it from the optimal distinguishability according to Helstrom's theorem. Furthermore, invoking ideas from classical and quantum Shannon theor…
Steganography is the process of hiding secret information by embedding it in an "innocent" message. We present protocols for hiding quantum information in a codeword of a quantum error-correcting code passing through a channel. Using either a shared classical secret key or shared entanglement the sender (Alice) disguises her information as errors in the channel. The receiver (Bob) can retrieve the hidden information, but an eavesdropper (Eve) with the power to monitor the channel, but without the secret key, cannot distinguish the message from channel noise. We analyze how difficult it is for …
We study uncloneable quantum encryption schemes for classical messages as recently proposed by Broadbent and Lord. We focus on the information-theoretic setting and give several limitations on the structure and security of these schemes: Concretely, 1) We give an explicit cloning-indistinguishable attack that succeeds with probability $\frac12 + μ/16$ where $μ$ is related to the largest eigenvalue of the resulting quantum ciphertexts. 2) For a uniform message distribution, we partially characterize the scheme with the minimal success probability for cloning attacks. 3) Under natural symmetry c…
Asymptotic Entanglement Hiding under Stabilizer Restrictions
School of Computer Science and Technology, University of Science and Technology of China（中国科学技术大学计算机科学与技术学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；School of Software Engineering, University of Science and Technology of China（中国科学技术大学软件工程学院）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）
We introduce a new type of cryptographic primitive that we call hiding fingerprinting. A (quantum) fingerprinting scheme translates a binary string of length $n$ to $d$ (qu)bits, typically $d\ll n$, such that given any string $y$ and a fingerprint of $x$, one can decide with high accuracy whether $x=y$. Classical fingerprinting schemes cannot hide information very well: a classical fingerprint of $x$ that guarantees error at most $ε$ necessarily reveals $Ω(\log(1/ epsilon))$ bits about $x$. We call a scheme hiding if it reveals $o(\log(1/ε))$ bits; accordingly, no classical scheme is hiding. F…
We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints, perform in the task of discriminating two multipartite quantum states. We mainly address the following question regarding the behaviour of these distinguishability norms in the high-dimensional regime: On a bipartite space, what are the relative strengths of standard classes of locally restricted measurements? We show that the class of PPT measurements typical…
