Quantifying nonorthogonality

An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle density matrices using methods that are similar to recently introduced techniques for quantifying entanglement. Several interesting special cases are considered. It is pointed out that a measure of nonorthogonality can meaningfully be associated with a single mixed quantum state. It is then shown how nonorthogonality can be unlocked with classical information; this analysis reveals interesting inequalities and points to a number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.

A new class of entanglement measures

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains Sections 1-5 & 7 of the previous version. The previous Section 6 is now in quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501

Relations between Entropies Produced in Nondeterministic Thermodynamic Processes

Landauer's erasure principle is generalized to nondeterministic processes on systems having an arbitrary number of non-symmetrical logical states. The condition that the process is applied in the same way, irrespective of the initial logical state, imposes some restrictions on the individual heat exchanges associated with each possible transition. The complete set of such restrictions are derived by a statistical analysis of the phase-space flow induced by the process. Landauer's erasure principle can be derived from and is a special case of these.Comment: 12 pages with one figure; a final major revision in presentation; physical assumptions are clarified no

Classical Concepts in Quantum Programming

The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the increasing hardware complexity and fully exploit its potential. This paper investigates, how classical concepts like hardware abstraction, hierarchical programs, data types, memory management, flow of control and structured programming can be used in quantum computing. The experimental language QCL will be introduced as an example, how elements like irreversible functions, local variables and conditional branching, which have no direct quantum counterparts, can be implemented, and how non-classical features like the reversibility of unitary transformation or the non-observability of quantum states can be accounted for within the framework of a procedural programming language.Comment: 11 pages, 4 figures, software available from http://tph.tuwien.ac.at/~oemer/qcl.html, submitted for QS2002 proceeding

Quantum cryptography with squeezed states

A quantum key distribution scheme based on the use of displaced squeezed vacuum states is presented. The states are squeezed in one of two field quadrature components, and the value of the squeezed component is used to encode a character from an alphabet. The uncertainty relation between quadrature components prevents an eavesdropper from determining both with enough precision to determine the character being sent. Losses degrade the performance of this scheme, but it is possible to use phase-sensitive amplifiers to boost the signal and partially compensate for their effect.Comment: 15 pages, no figure

Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles

A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in p+1 bases (not necessarily the same ones), and totally entangled in the remaining p^N-p. It follows that the maximum number of product bases is p+1, and when this number is realized, all remaining p^N-p bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for two qupits (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits and qutrits. With three qupits there are three MUB types, and a number of combinations (p+2) are possible in full complements. With N=4, there are 6 MUB types for p=2, but new MUB types become possible with larger p, and these are essential to the realization of full complements. With this example, we argue that new MUB types, showing new entanglement characteristics, should enter with every step in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs should play critical roles in filling complements.Comment: 27 pages, one figure, to be submitted to Physical Revie

Implementable Quantum Bit-String Commitment Protocol

Quantum bit-string commitment[A.Kent, Phys.Rev.Lett., 90, 237901 (2003)] or QBSC is a variant of bit commitment (BC). In this paper, we propose a new QBSC protocol that can be implemented using currently available technology, and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.Comment: To appear in Phys. Rev. A., 9 pages, 2 figure

A non-adiabatic approach to entanglement distribution over long distances

Entanglement distribution between trapped-atom quantum memories, viz. single atoms in optical cavities, is addressed. In most scenarios, the rate of entanglement distribution depends on the efficiency with which the state of traveling single photons can be transferred to trapped atoms. This loading efficiency is analytically studied for two-level, $V$-level, $\Lambda$-level, and double-$\Lambda$-level atomic configurations by means of a system-reservoir approach. An off-resonant non-adiabatic approach to loading $\Lambda$-level trapped-atom memories is proposed, and the ensuing trade-offs between the atom-light coupling rate and input photon bandwidth for achieving a high loading probability are identified. The non-adiabatic approach allows a broad class of optical sources to be used, and in some cases it provides a higher system throughput than what can be achieved by adiabatic loading mechanisms. The analysis is extended to the case of two double-$\Lambda$ trapped-atom memories illuminated by a polarization-entangled biphoton.Comment: 15 pages, 15 figure

Quantum cobwebs: Universal entangling of quantum states

Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA state, local operation and classical communication we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state. We quantify the amount of classical and quantum resources required to create universal entangled states. This is possibly a strongest form of quantum bit hiding with multiparties.Comment: Invited talk in II Winter Institute on FQTQO: Quantum Information Processing, held at S. N. Bose Center for Basic Science, Kolkata, during Jan 2-11, 2002. (To appear in Pramana-J. of Physics, 2002.