Is Amino-Acid Homochirality Due To Asymmetric Photolysis In Space?

Amino acids occurring in proteins are, with rare exceptions, exclusively of the L-configuration. Among the many scenarios put forward to explain the origin of this chiral homogeneity (i.e., homochirality), one involves the asymmetric photolysis of amino acids present in space, triggered by circularly polarized UV radiation. The recent observation of circularly polarized light (CPL) in the Orion OMC-1 star-forming region (Bailey et al. 1998, Science 281, 672) has been presented as providing a strong validation of this scenario. The present paper reviews the situation. It is stressed for example that one important condition for the asymmetric photolysis by CPL to be at the origin of the terrestrial homochirality of natural amino acids is generally overlooked, namely, the asymmetric photolysis should favour the L-enantiomer for ALL the primordial amino acids involved in the genesis of life (i.e., biogenic amino acids). Although this condition is probably satisfied for aliphatic amino acids, some non-aliphatic amino acids like tryptophan and proline may violate the condition and thus invalidate the asymmetric photolysis scenario, assuming they were among the primordial amino acids. Alternatively, if CPL photolysis in space is indeed the source of homochirality of amino acids, then tryptophan and proline may be crossed out from the list of biogenic amino acids.Comment: To appear in Space Science Reviews, 11 pages, 1 figure (LaTeX

Entropic Bell inequalities

We derive entropic Bell inequalities from considering entropy Venn diagrams. These entropic inequalities, akin to the Braunstein-Caves inequalities, are violated for a quantum-mechanical Einstein-Podolsky-Rosen pair, which implies that the conditional entropies of Bell variables must be negative in this case. This suggests that the satisfaction of entropic Bell inequalities is equivalent to the non-negativity of conditional entropies as a necessary condition for separability

Reduced randomness in quantum cryptography with sequences of qubits encoded in the same basis

We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.Comment: 8 pages, submitted to PR

On the von Neumann capacity of noisy quantum channels

We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the "Kholevo capacity") when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum "depolarizing" channel. The von Neumann capacity is interpreted within the context of superdense coding, and an "extended" Hamming bound is derived that is consistent with that capacity.Comment: 15 pages RevTeX with psfig, 13 figures. Revised interpretation of capacity, added section, changed titl

Prolegomena to a non-equilibrium quantum statistical mechanics

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.Comment: 20 pages, LaTeX with elsart.cls, 8 postscript figures. Special issue on quantum computation of Chaos, Solitons, and Fractal

Quantum conditional operator and a criterion for separability

We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite system is invariant under local unitary transformations and reflects its inseparability. More specifically, it is shown that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. This leads us to consider a related separability criterion based on the positive map $\Gamma:\rho \to (Tr \rho) - \rho$, where $\rho$ is an Hermitian operator. Any separable state is mapped by the tensor product of this map and the identity into a non-negative operator, which provides a simple necessary condition for separability. In the special case where one subsystem is a quantum bit, $\Gamma$ reduces to time-reversal, so that this separability condition is equivalent to partial transposition. It is therefore also sufficient for $2\times 2$ and $2\times 3$ systems. Finally, a simple connection between this map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe

Economical quantum cloning in any dimension

The possibility of cloning a d-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine found in [Phys. Rev. A {\bf 60}, 2764 (1999)] for qubits. We prove the impossibility of constructing an economical version of the optimal universal cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional phase-covariant cloner, which optimally clones all uniform superpositions, can be realized economically only in dimension d=2. The used ansatz is supported by numerical evidence up to d=7. An economical phase-covariant cloner can nevertheless be constructed for d>2, albeit with a lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.Comment: 8 pages RevTe

Broadcasting of three qubit entanglement via local copying and entanglement swapping

In this work,We investigate the problem of secretly broadcasting of three-qubit entangled state between two distant partners. The interesting feature of this problem is that starting from two particle entangled state shared between two distant partners we find that the action of local cloner on the qubits and the measurement on the machine state vector generates three-qubit entanglement between them. The broadcasting of entanglement is made secret by sending the measurement result secretly using cryptographic scheme based on orthogonal states. Further we show that this idea can be extended to generate three particle entangled state between three distant partners.Comment: 18 pages, 4 figures, Accepted in Physical Review