Masao Osaki

Accessible information and optimal strategies for real symmetrical quantum sources

We study the problem of optimizing the Shannon mutual information for sources of real quantum states, i.e., sources for which there is a basis in which all of the states have only real components. We consider in detail the sources

Quantum detection and mutual information for QAM and PSK signals

{\mathcal{E}}_{M}

The maximum mutual information without coding for binary quantum-state signals

of M equiprobable quantum bit (qubit) states lying symmetrically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real group-covariant sources for which the group acts irreducibly on the subset of all real states and prove the existence of a real group-covariant optimal strategy, extending a theorem of Davies [E. B. Davies, IEEE. Inf. Theory IT-24, 596 (1978)]. Finally, we propose an optical scheme to implement our optimal strategies, simple enough to be realized with present technology.

Optimizations of quantum measurement processes for signal detection and information transmission in quantum systems

We analyze the performance of the error probability and the mutual information for quadrature amplitude modulation (QAM) and phase-shift keying systems based on quantum detection theory. It is shown that the quantum receiver called square root measurement gives about 5.7 dB improvement in power in comparison with the classical one. Furthermore, we show that the quantum QAM system can achieve the same reliability as the conventional intensity modulation-direct detection (IM-DD) system with almost equal power, compressing the required bandwidth, while the reliability is degraded in general.

Derivation of classical capacity of a quantum channel for a discrete information source

The maximum mutual information without coding is investigated for binary quantum-state signals. The necessary condition for detection operators to represent the information optimal detection is satisfied for M-ary symmetric quantum-state signals by the detection operators derived from the quantum minimax strategy while its purpose is a minimization of the error probability. The true maximum mutual information is numerically analysed for the binary case.

On Reconciliation of Discrepant Sequences Shared through Quantum Mechanical Channels

Abstract The calculation method proposed here obtains an optimum detection process for an M-ary signal whose quantum states are linearly independent and nonorthogonal. Optimizations are carried out by minimizing the average probability of error or by maximizing the mutual information in the signal detection process. Quantum detection operators, in terms of which the signal detection process is mathematically described, are assumed to be projection operators defined on a Hilbert space H s spanned by the quantum states of the signal; that is, the best projection operators that describe the signal detection process are obtained. The optimization procedure is equivalent to finding an appropriate unitary transformation in the Hilbert space H s. For a binary quantum state signal, the optimum detection processes in which the average probability of error is minimized and in which the mutual information is maximized are obtained. It is found that the optimum detection process minimizing the average probability of ...

Realization of a Conditional Unitary Process by Systems of Collett and Knight

Abstract We prove that the classical capacity of a quantum channel for M symmetric states is achieved by a uniform distribution on a priori probabilities. We also investigate nonsymmetric cases such as a ternary amplitude shift keyed signal set and a 16-ary quadrature amplitude modulated signal set in coherent states.

On Maximum Mutual Information without Coding

In the practical quantum key distribution system, discrepancies may occur on the secret random sequences shared through a quantum mechanical channel even in the absence of an eavesdropper because of an imperfect system configuration and noises. The discrepancies may be spread and expanded through a following privacy amplification. Therefore all the discrepancies must be removed at this point. The reconciliation protocol was proposed by Bennett et al. As long as the authors know, however, detailed investigation on the protocol has not been reported. In this report, we investigate the reconciliation protocol proposed by Bennett et al. and consider to optimize it.

Optimum Binary Signal Detections for Error Probability and Mutual Information

Abstract This paper presents a physical interpretation of a conditional unitary process discussed in recent articles by one of the authors. It is verified that a generation process of a coherent squeezed state with arbitrary amplitude always corresponds to the conditional unitary process. Some examples of a quasi-free system are given.

On an Effectiveness of Quantum Mini-Max Formula in Quantum Communication

We consider the communication systems sending the classical (Shannon) information through the quantum channel. The classical information source X is represented with symbols and their a priori probabilities At a transmitter, each symbol is modulated to a quantum state and detected at a receiver by the quantum mechanically generalized measurement, so-called the probability operator-valued measure Here we call a detection operator since it represents a detection process deciding a received signal to be ‘j’. The detection operator is no-negative, and resolution of identity, where is the identity operator on the signal Hilbert space spanned by signal quantum states. This detection process can be regarded as a quantum channel characterized by the conditional probability defined as follows: