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arXiv:1108.4163 · Quantum Measurements and Quantum Metrology

Error Free Quantum Reading by Quasi Bell State of Entangled Coherent States

Osamu Hirota

Published Dec 20, 2017• 28 citations
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Abstract

Abstract Nonclassical states of light field have been exploited to provide marvellous results in quantum information science. Usefulness of nonclassical states in quantum information science depends on whether a physical parameter as a signal is continuous or discrete. Here we present an investigation of the potential of quasi Bell states of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola (Phys.Rev.Lett.,106,090504,2011). This is a typical example of discrimination for discrete quantum parameters. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.

DOI
10.1515/qmetro-2017-0009

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Quasi Bell State of Entangled Coherent States in Quantum Reading

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Non-classical states of light field have been exploited to provide marvellous results in quantum information science. Effectiveness of nonclassical states depends on whether physical parameter as signal is continuous or digital. Here we present an investigation on the potential of quasi Bell state of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola. This is a typical example of discrete quantum discrimination. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.

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Abstract Nonclassical states of light field have been exploited to provide marvellous results in quantum information science. Usefulness of nonclassical states in quantum information science depends on whether a physical parameter as a signal is continuous or discrete. Here we present an investigation of the potential of quasi Bell states of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola (Phys.Rev.Lett.,106,090504,2011). This is a typical example of discrimination for discrete quantum parameters. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.
Non-classical states of light field have been exploited to provide marvellous results in quantum information science. Effectiveness of nonclassical states depends on whether physical parameter as signal is continuous or digital. Here we present an investigation on the potential of quasi Bell state of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola. This is a typical example of discrete quantum discrimination. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.
Quantum reading is the protocol that uses entanglement for reading a bit stored in digital memory. By using entanglement, it was shown by S. Pirandola that the data rate was improved. O. Hirota showed that in noiseless environments, error-free reading is possible by using a quasi-Bell state that has maximum entanglement. After that, some non-ideal cases were considered, such as symmetric loss and incomplete phase shift. In this study, we would like to clarify properties of the protocol in more realistic situations for experiment. In this paper, we compare and consider the effects using maximum and non-maximum quasi-Bell states on quantum reading with (1) only non-symmetric loss, (2) non-symmetric loss and incomplete phase shift, and (3) non-symmetric loss and phase noise. In the case (1), we derive the exact solutions of the error probabilities when using maximum and non-maximum quasi-Bell states. Then we clarify that the error probability using maximum quasi-Bell states is always lower than that using non-maximum quasi-Bell states. In the other two cases, we compute error probabilities numerically. In cases (2) and (3), the results are different from that of the case (1). That is, both maximum and non-maximum quasi-Bell states are not always supremer than the other.
It has been shown recently S. Pirandola [Phys. Rev. Lett. 106, 090504 (2011)] that entangled light with Einstein-Podolsky-Rosen correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of a reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of a continuous variable Gaussian setting for its analysis when arbitrary values of reflectivities $0\ensuremath{\le}{r}_{0},{r}_{1}\ensuremath{\le}1$ are considered. Here we restrict ourselves to a basic quantum readout mechanism with two different families of non-Gaussian entangled states of light, in which the binary channels to be discriminated are (i) ideal memory characterized by reflectivity r1=1{r}_{1}=1r1​=1 (identity channel) and (ii) a thermal noise channel---where the signal light illuminating the memory location gets completely lost (r0=0{r}_{0}=0r0​=0) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of two families of non-Gaussian entangled light [($m,{m}^{\ensuremath{'}}$) family of path-entangled photon states and entangled state obtained by mixing a single photon with coherent light in a 50:50 beam splitter] with any classical source of light in this model. We identify that the classes of non-Gaussian entangled transmitters studied here offer significantly better reading performance than any classical transmitters of light in the regime of low signal intensity. We also demonstrate that the ($m,{m}^{\ensuremath{'}}$) family of entangled light exhibits better reading performance than NOON states.
It has been reported that error-free quantum reading of a classical digital memory is possible when the entangled coherent state |a〉 |a〉– |– a〉|–a〉 is used as the probe state for quantum reading with binary phase shift keying format under the assumption that the channel is noiseless [quant-ph/1108.4163v2]. In this paper, the theoretical performance limits of the minimum error probability and classical capacity of quantum reading with binary phase shift keying entangled coherent state signal are investigated in the presence of channel loss.
Quantum reading is one of application protocols of entanglement. This protocol uses entanglement for reading of a digital memory such as a CD or DVD. O. Hirota showed that in a noiseless environment, quantum reading using a quasi-Bell state that has maximum entanglement is error free. Moreover, K. Kato and O. Hirota considered equal losses for amplitudes of modes A and B of this state in determining energy-loss effects. However, in real settings, the loss associated with the amplitude of mode B is greater than that of mode A. Therefore, we consider non-symmetric loss and its effect on quantum reading using a quasi-Bell state. In this paper, we show the analytical solution of the error probability in this case, and investigate the amplitude of mode A that minimizes the error probability when the amplitude of mode B is fixed. Moreover, we consider the robustness against alignment mismatch.
The readout of a classical memory can be modelled as a problem of quantum channel discrimination, where a decoder retrieves information by distinguishing the different quantum channels encoded in each cell of the memory (Pirandola 2011 Phys. Rev. Lett. 106 090504). In the case of optical memories, such as CDs and DVDs, this discrimination involves lossy bosonic channels and can be remarkably boosted by the use of nonclassical light (quantum reading). Here we generalize these concepts by extending the model of memory from single-cell to multi-cell encoding. In general, information is stored in a block of cells by using a channel-codeword, i.e. a sequence of channels chosen according to a classical code. Correspondingly, the readout of data is realized by a process of 'parallel' channel discrimination, where the entire block of cells is probed simultaneously and decoded via an optimal collective measurement. In the limit of a large block we define the quantum reading capacity of the memory, quantifying the maximum number of readable bits per cell. This notion of capacity is nontrivial when we suitably constrain the physical resources of the decoder. For optical memories (encoding bosonic channels), such a constraint is energetic and corresponds to fixing the mean total number of photons per cell. In this case, we are able to prove a separation between the quantum reading capacity and the maximum information rate achievable by classical transmitters, i.e. arbitrary classical mixtures of coherent states. In fact, we can easily construct nonclassical transmitters that are able to outperform any classical transmitter, thus showing that the advantages of quantum reading persist in the optimal multi-cell scenario.