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Register a new userReversible Simulation of Irreversible Computation by Pebble Games
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Reversible simulation of irreversible algorithms is analyzed in the stylized form of a `reversible pebble game. While such simulations incur little overhead in additional computation time, they use a large amount of additional memory space during the computation. The reacheable reversible simulation instantaneous descriptions (pebble configurations) are characterized completely. As a corollary we obtain the reversible simulation by Bennett and that among all simulations that can be modelled by the pebble game, Bennetts simulation is optimal in that it uses the least auxiliary space for the greatest number of simulated steps. One can reduce the auxiliary storage overhead incurred by the reversible simulation at the cost of allowing limited erasing leading to an irreversibility-space tradeoff. We show that in this resource-bounded setting the limited erasing needs to be performed at precise instants during the simulation. We show that the reversible simulation can be modified so that it is applicable also when the simulated computation time is unknown.
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Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {bf S}$_{2^w}$. The permutation group P($n$), isomorphic to {bf S}$_n$, contains cycles with length~$p$, ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By Lagrange interpolation between the $p$~matrices of the cycle, we step from a finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the unitary group U($n$). As U($2^w$) is the group of all possible quantum circuits, acting on $w$~qubits, such interpolation is a natural way to step from classical computation to quantum computation.
The CHSH no-signalling game studies Bell nonlocality by showcasing a gap between the win rates of classical strategies, quantum-entangled strategies, and no-signalling strategies. Similarly, the CHSH* single-system game explores the advantage of irreversible processes by showcasing a gap between the win rates of classical reversible strategies, quantum reversible strategies, and irreversible strategies. The irreversible process of erasure rules supreme for the CHSH* single-system game, but this ``erasure advantage does not necessarily extend to every single-system game: We introduce the 32-Game, in which reversibility is irrelevant and only the distinction between classical and quantum operations matters. We showcase our new insight by modifying the CHSH* game to make it erasure-immune, while conserving its quantum advantage. We conclude by the reverse procedure: We tune the 32-Game to make it erasure-vulnerable, and erase its quantum advantage in the process. The take-home message is that, when the size of the single-system is too small for Alice to encode her whole input, quantum advantage and erasure advantage can happen independently.
We study properties of quantum strategies, which are complete specifications of a given partys actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamio{l}kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaevs lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.
Steganography (literally meaning covered writing) is the art and science of embedding secret message into seemingly harmless message. Stenography is practice from olden days where in ancient Greece people used wooden blocks to inscribe secret data and cover the date with wax and write normal message on it. Today stenography is used in various field like multimedia, networks, medical, military etc. With increasing technology trends steganography is becoming more and more advanced where people not only interested on hiding messages in multimedia data (cover data) but also at the receiving end they are willing to obtain original cover data without any distortion after extracting secret message. This paper will discuss few irreversible data hiding techniques and also, some recently proposed reversible data hiding approach using images.
We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of permutational quantum computation of Jordan[1, 2]. (3) With postselection, the model is equivalent to PostBQP.
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