An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ``Alice,'' receiver, ``Bob,'' must prearrange sharing of an EPR-correlated pair particles. Alice makes a joint measurement on her EPR particle system, sends Bob result this measurement. Knowing this, convert his into exact replica which destroyed.

A class of problems is described which can be solved more efficiently by quantum computation than any classical or stochastic method. The solves the problem with certainty in exponentially less time deterministic computation.

Abstract We propose a definition of fidelity for mixed quantum states in terms Uhlmann's ‘transition probability’ formula F(ϱ1, ϱ2) = {trace [(√ϱ1ϱ2 × √ϱ1)1/2]}2 and give new elementary proofs its essential properties.

Current technology is beginning to allow us manipulate rather than just observe individual quantum phenomena. This opens up the possibility of exploiting effects perform computations beyond scope any classical computer. Recently Peter Shor discovered an efficient algorithm for factoring whole numbers, which uses characteristically effects. The illustrates potential power computation, as there no known method solving this problem. authors give exposition Shor's together with introduction...

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on communication channel. Although become if supplemented by classical privacy-amplification techniques, resulting difficult to analyze and have not been proved secure. We introduce concept privacy amplification a scheme incorporating it which is provably secure over noisy The uses an ``entanglement purification'' procedure which, because requires only few controlled-not single-qubit operations,...

Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks general information processing systems which have recently been shown to many interesting non--classical properties. We describe a simple gate, controlled--NOT, and analyse some its applications. discuss two possible physical realisations gate; one based on Ramsey atomic interferometry other selective driving optical resonances subsystems undergoing dipole--dipole interaction.

We show that, given a general mixed state for quantum system, there are no physical means broadcasting that onto two separate systems, even when the need only be reproduced marginally on systems. This result extends standard no-cloning theorem pure states.

We give a constructive proof that all mixed states of N qubits in sufficiently small neighborhood the maximally state are separable. The construction provides an explicit representation any such as mixture product states. upper and lower bounds on size neighborhood, which show its extent decreases exponentially with number qubits. also discuss implications for NMR quantum computing.

For any quantum algorithm operating on pure states, we prove that the presence of multi‐partite entanglement, with a number parties increases unboundedly input size, is necessary if to offer an exponential speed‐up over classical computation. Furthermore, can be efficiently simulated classically within prescribed tolerance η even suitably small amount global entanglement present. We explicitly identify occurrence increasing in Shor's algorithm. Our results do not apply algorithms mixed...

We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' states, e.g., certain photon polarizations, together with specified set probabilities which these states must be sent. If receiver restricted to making separate measurements on received ``letter'' then Kholevo theorem implies that amount transmitted per letter cannot greater than von Neumann entropy H ensemble. In fact actual will usually significantly less H. show,...

In the weak value formalism of Aharonov et al., ${A}_{w}$ any observable $A$ is generally a complex number. We derive physical interpretation its in terms shift measurement pointer's mean position and momentum. particular, we show that contains term jointly proportional to imaginary part rate at which pointer spreading space as it enters interaction.

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically, we introduce class post-IQP languages decided with bounded error uniform families circuits post-selection, prove first equals PP. Using this result show if circuit could classically efficiently sampled, either exactly in...

We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, classical communications, to establish a synchronized pair of atomic clocks. In contrast synchronization schemes, the accuracy our protocol is independent Alice's or Bob's knowledge their relative locations properties intervening medium.

Abstract We give an account of the quantum noiseless coding theorem, including a new proof based on simplified block scheme. also discuss illustrative example coding.

We propose a method for the stabilization of quantum computations (including state storage). The is based on operation projection into $\cal SYM$, symmetric subspace full space R redundant copies computer. describe an efficient algorithm and network effecting SYM$--projection discuss stabilizing effect proposed in context unitary errors generated by hardware imprecision, nonunitary arising from external environmental interaction. Finally, limitations are discussed.

We discuss the fundamental role of entanglement as essential nonclassical feature providing computational speed-up in known quantum algorithms. review construction Fourier transform on an Abelian group and principles underlying fast algorithm. describe implementation FFT algorithm for integers modulo 2^n context, showing how group-theoretic formalism leads to standard network identifying property that gives rise exponential speedup (compared classical FFT). Finally we outline use extracting...

The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. general construction transform an Abelian group is outlined this provides unified understanding efficacy algorithms. Finally we describe efficient factoring algorithm based formalism Kitaev contrast its structure to ingredients Shor' algorithm.

It has long been known that the von Neumann entropy S is an upper bound on information one can extract from a quantum system in unknown pure state. In this paper we define ``subentropy'' Q, which prove to be lower information. Moreover, just as best depends only density matrix, show Q matrix. Other parallels between and are also demonstrated.

We describe a complete protocol for bit commitment based on the transmission of polarized photons. show that under laws quantum physics, this cannot be cheated by either party except with exponentially small probability (exponential in running time needed to implement honest protocol). A more thorough analysis is required adjust all constants used paper get best performance from our construction. Better performances may probably achieved using third conjugate transmission-reception basis...

In the formalism of measurement based quantum computation we start with a given fixed entangled state many qubits and perform by applying sequence measurements to designated in bases. The choice basis for later may depend on earlier outcomes final result is determined from classical data all outcomes. This contrast more familiar gate array model which computational steps are unitary operations, developing large prior some output. Two principal schemes teleportation (TQC) so-called cluster or...

Let G ( A , B ) denote the two-qubit gate that acts as one-qubit SU (2) gates and in even odd parity subspaces, respectively, of two qubits. Using a Clifford algebra formalism, we show arbitrary uniform families circuits these gates, restricted to act only on nearest neighbour (n.n.) qubit lines, can be classically efficiently simulated. This reproduces result originally proved by Valiant using his matchgate subsequently related others free fermionic physics. We further if n.n. condition is...