arXiv subjects

Stephen M. Barnett

Publications and source records attributed to Stephen M. Barnett.

At least 109 records · Page 6Linked to original sources

arXiv2002

Comparison of two unknown pure quantum states

We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to conclusively identify two pure unknown states as being identical, and construct the optimal measurement for conclusively identifying them as being different. We then derive optimal strategies for state comparison when the state of each system is one of two known states.

quant-ph↗

arXiv2002

Maximum Fidelity Retransmission of Mirror Symmetric Qubit States

In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this process is the fidelity, which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state. We consider the maximisation of the fidelity for a set of three mirror symmetric qubit states. In contrast to previous examples, we find that the strategy which minimises the probability of erroneously identifying the state does not generally maximise the fidelity.

quant-ph↗

arXiv2002

Comparison of unitary transforms

We analyze the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such comparisons without obtaining any information about the individual transformations. Different comparison strategies are presented and compared with respect to their efficiency. With an interferometric setup, it is possible to compare two unitary transforms using only one test particle. Another strategy makes use of a two-particle singlet state. This strategy is more efficient than using a non-entangled two-particle test state, thus demonstrating the benefit of entanglement. Generalisations to higher dimensional transforms and to more than two transformations are made.

quant-ph↗

arXiv2002

Quantum retrodiction in open systems

Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum mechanics. Recent interest in quantum communications and cryptography, however, has provided retrodiction with a potential practical application. For this purpose quantum retrodiction in open systems should be more relevant than in closed systems isolated from the environment. In this paper we study retrodiction in open systems and develop a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities. We solve the master equation, by way of example, for the driven two-level atom coupled to the electromagnetic field.

quant-ph↗

arXiv2002

Retrodiction with two-level atoms: atomic previvals

In the Jaynes-Cummings model a two-level atom interacts with a single-mode electromagnetic field. Quantum mechanics predicts collapses and revivals in the probability that a measurement will show the atom to be excited at various times after the initial preparation of the atom and field. In retrodictive quantum mechanics we seek the probability that the atom was prepared in a particular state given the initial state of the field and the outcome of a later measurement on the atom. Although this is not simply the time reverse of the usual predictive problem, we demonstrate in this paper that retrodictive collapses and revivals also exist. We highlight the differences between predictive and retrodictive evolutions and describe an interesting situation where the prepared state is essentially unretrodictable.

quant-ph↗

arXiv2002

Quantum theory of preparation and measurement

The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.

quant-ph↗

arXiv2002

Retrodiction as a tool for micromaser field measurements

We use retrodictive quantum theory to describe cavity field measurements by successive atomic detections in the micromaser. We calculate the state of the micromaser cavity field prior to detection of sequences of atoms in either the excited or ground state, for atoms that are initially prepared in the excited state. This provides the POM elements, which describe such sequences of measurements.

quant-ph↗

arXiv2002

Macroscopic quantum fluctuations in noise-sustained optical patterns

We investigate quantum effects in pattern-formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based linearization about a pseudo-classical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a $c$-number variable but is driven by the $c$-number representation of the quantum sub-harmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the non-classical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further above threshold the macroscopic quantum noise suppresses these effects.

quant-ph↗

arXiv2002

Analytic stochastic treatment of a nonlinear quantum model with negative diffusion

We apply a proposal of Yuen and Tombesi, for treating stochastic problems with negative diffusion, to the analytically soluble problem of the single-mode anharmonic oscillator. We find that the associated stochastic realizations include divergent trajectories. It is possible, however, to solve the stochastic problem exactly, but the averaging must be performed with great care.

quant-ph↗

arXiv2002

Optimal parameter estimation of depolarizing channel

We investigate strategies for estimating a depolarizing channel for a finite dimensional system. Our analysis addresses the double optimization problem of selecting the best input probe state and the measurement strategy that minimizes the Bayes cost of a quadratic function. In the qubit case, we derive the Bayes optimal strategy for any finite number of input probe particles when bipartite entanglement can be formed in the probe particles.

quant-ph↗

arXiv2002

Minimum-error discrimination between three mirror-symmetric states

We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested.

quant-ph↗

arXiv2001

Optimum detection for extracting maximum information from symmetric qubit sets

We demonstrate a class of optimum detection strategies for extracting the maximum information from sets of equiprobable real symmetric qubit states of a single photon. These optimum strategies have been predicted by Sasaki et al. [Phys. Rev. A{\bf 59}, 3325 (1999)]. The peculiar aspect is that the detections with at least three outputs suffice for optimum extraction of information regardless of the number of signal elements. The cases of ternary (or trine), quinary, and septenary polarization signals are studied where a standard von Neumann detection (a projection onto a binary orthogonal basis) fails to access the maximum information. Our experiments demonstrate that it is possible with present technologies to attain about 96% of the theoretical limit.

quant-ph↗

arXiv2001

Conditional beam splitting attack on quantum key distribution

We present a novel attack on quantum key distribution based on the idea of adaptive absorption [calsam01]. The conditional beam splitting attack is shown to be much more efficient than the conventional beam spitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam splitting attack, based solely on linear optical elements, is well within reach of current technology.

quant-ph↗

arXiv2001

Master Equation for Retrodiction of Quantum Communication Signals

We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements, which has particular relevance to quantum communication.

quant-ph↗

arXiv2001

Fidelity and the communication of quantum information

We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve {\it classical} information and the fidelity measures the retrieval of {\it quantum} information. We present the optimal measurement strategies for maximising the fidelity given a source that encodes information on the symmetric qubit-states.

quant-ph↗

arXiv2001

Atomic Retrodiction

Measurement of a quantum system provides information concerning the state in which it was prepared. In this paper we show how the retrodictive formalism can be used to evaluate the probability associated with any one of a given set of preparation events. We illustrate our method by calculating the retrodictive density operator for a two-level atom coupled to the electromagnetic field.

quant-ph↗

arXiv2001

Bayes' theorem and quantum retrodiction

We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalised probability operator measure element associated with the result. We examine applications to quantum optical cryptography and to the optical beam splitter.

quant-ph↗

arXiv2001

Removal of a single photon by adaptive absorption

We present a method to remove, using only linear optics, exactly one photon from a field-mode. This is achieved by putting the system in contact with an absorbing environment which is under continuous monitoring. A feedback mechanism then decouples the system from the environment as soon as the first photon is absorbed. We propose a possible scheme to implement this process and provide the theoretical tools to describe it.

quant-ph↗