Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2010
We study a bosonic Gaussian channel with classical additive noise and memory effects. In particul... more We study a bosonic Gaussian channel with classical additive noise and memory effects. In particular we consider correlations in the added noise which are asymmetric in the phase space quadratures and show in such a case the usefulness of entangled codewords for reliable communication. We explicitly demonstrate that optimal rates can be achieved with multiparty entangled codewords.
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachi... more Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
2011 IEEE Photonics Society Summer Topical Meeting Series, 2011
ABSTRACT We introduce ultrafast information coding on multiple orthogonal pulse modes, using wave... more ABSTRACT We introduce ultrafast information coding on multiple orthogonal pulse modes, using waveguided PDC sources emitting the required quantum states. We present optical pulse gates enabling state manipulation and (de)-multiplexing and analyze the obtained channel capacities.
Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentiall... more Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.
Quantum physics allows us to certify the security of a communication line against an eavesdropper... more Quantum physics allows us to certify the security of a communication line against an eavesdropper with unbounded computational power. The achievable rates of quantum secured communication are also limited by the laws of quantum physics and in particular by the properties of entanglement. For the most relevant case of a lossy communication line, this implies that the secret key generation rate vanishes at least exponentially with the distance. In this letter we show that this fundamental limitation can be violated by a constant amount if one seeks secrecy against an eavesdropper still endowed with unlimited computational power but capable of storing quantum information only for a limited time. Under this relaxed but still concrete security assumption, we show that the phenomenon of quantum data locking can be harnessed to bootstrap a 'locked' key at a rate as high as the eavesdropper's quantum discord. For the case of the lossy bononic channel, this yields a constant locked key generation rate of one bit per mode over arbitrarily long communication distances.
We show that, if the accessible information is taken as a security quantifier, a quantum channel ... more We show that, if the accessible information is taken as a security quantifier, a quantum channel can convey private messages at a tremendously high rate, as high as less than one bit below the rate of non-private classical communication. This result is obtained by using the quantum enigma machine, a cipher exploiting the quantum data locking effect. The price to pay to achieve such a high private communication rate is that accessible information-security is in general not composable, yet composable security holds against an eavesdropper with unlimited computation power but having a quantum memory with finite coherence time.
2013 IEEE Photonics Society Summer Topical Meeting Series, 2013
ABSTRACT Using ultrafast multimode PDC sources and optical quantum pulse gates based on engineere... more ABSTRACT Using ultrafast multimode PDC sources and optical quantum pulse gates based on engineered frequency conversion processes we introduce multiplexed quantum information coding and show that it enables an exponential increase in the achievable quantum communication rate.
International Conference on Quantum Information, 2011
ABSTRACT We introduce multiplexed information coding in quantum channels, using waveguided PDC so... more ABSTRACT We introduce multiplexed information coding in quantum channels, using waveguided PDC sources emitting the required quantum states. We analyze the obtained channel capacities, present a significant gain over single-mode coding, and enhanced loss resilience.
The locking effect is a phenomenon which is unique to quantum information theory and represents o... more The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking protocol harnesses this effect in a cryptographic context, whereby one party can encode n bits into n qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon's classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels' locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.
Any physical process can be represented as a quantum channel mapping an initial state into a fina... more Any physical process can be represented as a quantum channel mapping an initial state into a final state. Hence it can be characterized from the point of view of communication theory. Recently a lot of efforts have been devoted to encompass memory effects within this approach. It is usually meant that memory effects arise when the application of a channel on several inputs is not merely the result of identical and independent maps. Alternatively, if the channel is defined by its infinitesimal generator in a continuous-time description, one refers as well to memory effects if such an evolution is non-Markovian. The consideration of such effects has given rise to more powerful tools than the traditional quantum channel approaches for describing quantum information processes. Moreover it constitutes a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory with other branches of physics. Recent developments in the field of quantum channels and memory effects are here reviewed. PACS numbers: 03.67.-a, 89.70.-a, 02.50.-r A. Discrete memory channels 23 B. Continuous memory channels 26 VIII. Quantum channels from dynamics with memory 30 A. Non Markovian master equations 32 B. Legitimate memory kernels 32 C. Markovian vs non-Markovian dynamics 33 D. A solvable model 34 IX. Summary and Outlook 34 Acknowledgments 35 A. Tools for characterizing quantum channels 35 B. Entropic quantities 36 arXiv:1207.5435v3 [quant-ph] 20 Nov 2012 C. Decomposition for non-anticipatory quantum channels 37 D. C * -and Quasi-Local Algebras 37 References 38
2011 Conference on Lasers & Electro-Optics Europe & 12th European Quantum Electronics Conference CLEO EUROPE/EQEC, 2011
ABSTRACT We introduce multiplexed information coding in quantum channels, using ultrafast wavegui... more ABSTRACT We introduce multiplexed information coding in quantum channels, using ultrafast waveguided PDC sources emitting the required quantum states. We present an efficient method to characterize the high-dimensional PDC output, and evaluate their performance after losses.
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in or... more The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical exper... more Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.
ABSTRACT We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistic... more ABSTRACT We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistical model and compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We uncover that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened with respect to the chaoticity of the 3D Gaussian statistical model.
We introduce a general model for a lossy bosonic memory channel and calculate the classical and t... more We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.
We study maximally multipartite entangled states in the context of Gaussian continuous variable q... more We study maximally multipartite entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n = 2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n ≤ 7.
With increasing communication rates via quantum channels, memory effects become unavoidable whene... more With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable with the typical relaxation time of the channel environment. We then introduce a model of bosonic memory channel, describing correlated noise effects in quantum optical processes via attenuating or amplifying media. To study such a channel model we make use of a proper set of collective field variables, which allows us to unravel the memory effects, mapping the n-fold concatenation of the memory channel to a, unitarily equivalent, direct product of n single-mode bosonic channels. We hence estimate the channel capacities by relying on known results for the memoryless setting. Our findings show that the model is characterized by two different regimes, in which the cross-correlations induced by the noise among different channel uses are either exponentially enhanced or exponentially reduced.
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2010
We study a bosonic Gaussian channel with classical additive noise and memory effects. In particul... more We study a bosonic Gaussian channel with classical additive noise and memory effects. In particular we consider correlations in the added noise which are asymmetric in the phase space quadratures and show in such a case the usefulness of entangled codewords for reliable communication. We explicitly demonstrate that optimal rates can be achieved with multiparty entangled codewords.
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachi... more Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
2011 IEEE Photonics Society Summer Topical Meeting Series, 2011
ABSTRACT We introduce ultrafast information coding on multiple orthogonal pulse modes, using wave... more ABSTRACT We introduce ultrafast information coding on multiple orthogonal pulse modes, using waveguided PDC sources emitting the required quantum states. We present optical pulse gates enabling state manipulation and (de)-multiplexing and analyze the obtained channel capacities.
Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentiall... more Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.
Quantum physics allows us to certify the security of a communication line against an eavesdropper... more Quantum physics allows us to certify the security of a communication line against an eavesdropper with unbounded computational power. The achievable rates of quantum secured communication are also limited by the laws of quantum physics and in particular by the properties of entanglement. For the most relevant case of a lossy communication line, this implies that the secret key generation rate vanishes at least exponentially with the distance. In this letter we show that this fundamental limitation can be violated by a constant amount if one seeks secrecy against an eavesdropper still endowed with unlimited computational power but capable of storing quantum information only for a limited time. Under this relaxed but still concrete security assumption, we show that the phenomenon of quantum data locking can be harnessed to bootstrap a 'locked' key at a rate as high as the eavesdropper's quantum discord. For the case of the lossy bononic channel, this yields a constant locked key generation rate of one bit per mode over arbitrarily long communication distances.
We show that, if the accessible information is taken as a security quantifier, a quantum channel ... more We show that, if the accessible information is taken as a security quantifier, a quantum channel can convey private messages at a tremendously high rate, as high as less than one bit below the rate of non-private classical communication. This result is obtained by using the quantum enigma machine, a cipher exploiting the quantum data locking effect. The price to pay to achieve such a high private communication rate is that accessible information-security is in general not composable, yet composable security holds against an eavesdropper with unlimited computation power but having a quantum memory with finite coherence time.
2013 IEEE Photonics Society Summer Topical Meeting Series, 2013
ABSTRACT Using ultrafast multimode PDC sources and optical quantum pulse gates based on engineere... more ABSTRACT Using ultrafast multimode PDC sources and optical quantum pulse gates based on engineered frequency conversion processes we introduce multiplexed quantum information coding and show that it enables an exponential increase in the achievable quantum communication rate.
International Conference on Quantum Information, 2011
ABSTRACT We introduce multiplexed information coding in quantum channels, using waveguided PDC so... more ABSTRACT We introduce multiplexed information coding in quantum channels, using waveguided PDC sources emitting the required quantum states. We analyze the obtained channel capacities, present a significant gain over single-mode coding, and enhanced loss resilience.
The locking effect is a phenomenon which is unique to quantum information theory and represents o... more The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking protocol harnesses this effect in a cryptographic context, whereby one party can encode n bits into n qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon's classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels' locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.
Any physical process can be represented as a quantum channel mapping an initial state into a fina... more Any physical process can be represented as a quantum channel mapping an initial state into a final state. Hence it can be characterized from the point of view of communication theory. Recently a lot of efforts have been devoted to encompass memory effects within this approach. It is usually meant that memory effects arise when the application of a channel on several inputs is not merely the result of identical and independent maps. Alternatively, if the channel is defined by its infinitesimal generator in a continuous-time description, one refers as well to memory effects if such an evolution is non-Markovian. The consideration of such effects has given rise to more powerful tools than the traditional quantum channel approaches for describing quantum information processes. Moreover it constitutes a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory with other branches of physics. Recent developments in the field of quantum channels and memory effects are here reviewed. PACS numbers: 03.67.-a, 89.70.-a, 02.50.-r A. Discrete memory channels 23 B. Continuous memory channels 26 VIII. Quantum channels from dynamics with memory 30 A. Non Markovian master equations 32 B. Legitimate memory kernels 32 C. Markovian vs non-Markovian dynamics 33 D. A solvable model 34 IX. Summary and Outlook 34 Acknowledgments 35 A. Tools for characterizing quantum channels 35 B. Entropic quantities 36 arXiv:1207.5435v3 [quant-ph] 20 Nov 2012 C. Decomposition for non-anticipatory quantum channels 37 D. C * -and Quasi-Local Algebras 37 References 38
2011 Conference on Lasers & Electro-Optics Europe & 12th European Quantum Electronics Conference CLEO EUROPE/EQEC, 2011
ABSTRACT We introduce multiplexed information coding in quantum channels, using ultrafast wavegui... more ABSTRACT We introduce multiplexed information coding in quantum channels, using ultrafast waveguided PDC sources emitting the required quantum states. We present an efficient method to characterize the high-dimensional PDC output, and evaluate their performance after losses.
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in or... more The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical exper... more Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.
ABSTRACT We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistic... more ABSTRACT We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistical model and compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We uncover that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened with respect to the chaoticity of the 3D Gaussian statistical model.
We introduce a general model for a lossy bosonic memory channel and calculate the classical and t... more We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.
We study maximally multipartite entangled states in the context of Gaussian continuous variable q... more We study maximally multipartite entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n = 2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n ≤ 7.
With increasing communication rates via quantum channels, memory effects become unavoidable whene... more With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable with the typical relaxation time of the channel environment. We then introduce a model of bosonic memory channel, describing correlated noise effects in quantum optical processes via attenuating or amplifying media. To study such a channel model we make use of a proper set of collective field variables, which allows us to unravel the memory effects, mapping the n-fold concatenation of the memory channel to a, unitarily equivalent, direct product of n single-mode bosonic channels. We hence estimate the channel capacities by relying on known results for the memoryless setting. Our findings show that the model is characterized by two different regimes, in which the cross-correlations induced by the noise among different channel uses are either exponentially enhanced or exponentially reduced.
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Papers by Cosmo Lupo