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We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…
Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the…
A nonlocal bipartite unitary gate can sometimes be implemented using prior entanglement and only one round of classical communication in which the two parties send messages to each other simultaneously. This cuts the classical communication…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and…
Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a…
A long-standing question is whether it is possible to delegate computational tasks securely. Recently, both a classical and a quantum solution to this problem were found. Here, we study the interplay of classical and quantum approaches and…
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…
It is known that any bipartite unitary operator of Schmidt rank three is equivalent to a controlled unitary under local unitaries. We propose a standard form of such operators. Using the form we improve the upper bound for the entanglement…
This work introduces a relative diffusion transformation (RDT) - a simple unitary transformation which acts in a subspace, localized by an oracle. Such a transformation can not be fulfilled on quantum Turing machines with this oracle in…
Collective operations on a network of spatially-separated quantum systems can be carried out using local quantum (LQ) operations, classical communication (CC) and shared entanglement (SE). Such operations can also be used to communicate…
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the…
Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the…
We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…