ABSTRACT Bell's inequality makes a seemingly insane scenario possible --- devices of unkn... more ABSTRACT Bell's inequality makes a seemingly insane scenario possible --- devices of unknown or dubious provenance, even those that are manufactured by our enemies, can be safely used for secret communication. And this is for real! All that is needed to implement such a bizarre form of cryptography is a loophole-free violation of Bell's inequalities. It is on the edge of being technologically feasible. I will provide a brief overview of quantum and post-quantum cryptography and describe how studies of entanglement and the foundations of quantum theory influenced the way we may soon protect information.
This is a brief description of how to protect quantum states from dissipation and decoherence tha... more This is a brief description of how to protect quantum states from dissipation and decoherence that arise due to uncontrolled interactions with the environment. We discuss recoherence and stabilization 0f quantum states based on two techniques known as "symmetrization" and "quantum error correction". We illustrate our considerations with the most popular quantum-optical model of the system-environment interaction, commonly used to describe spontaneous emission, and show the benefits of quantum error correction in this case.
A computation is a physical process. It may be performed by a piece of electronics or on an abacu... more A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (qua... more Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state ρABE. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this scenario as a unification of two standard scenarios: (i) key distillation (agreement) from classical correlations and (ii) key distillation from pure tripartite quantum states. Firstly, we obtain generalisations of fundamental results related to scenarios (i) and (ii), including upper bounds on the key rate, i.e., the number of key bits that can be extracted per copy of ρABE. Moreover, based on an embedding of classical distributions into quantum states, we are able to find new connections between protocols and quantities in the standard scenarios (i) and (ii). Secondly, we study specific properties of key distillation protocols. In particular, we show that every protocol that makes use of pre-shared key can be transformed into an equally efficient protocol which needs no pre-shared key. This result is of practical significance as it applies to quantum key distribution (QKD) protocols, but it also implies that the key rate cannot be locked with information on Eve's side. Finally, we exhibit an arbitrarily large separation between the key rate in the standard setting where Eve is equipped with quantum memory and the key rate in a setting where Eve is only given classical memory. This shows that assumptions on the nature of Eve's memory are important in order to determine the correct security threshold in QKD.
Quantum computers require technologies that offer both sufficient control over coherent quantum p... more Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We argue, that photons confined to photonic crystals, and in particular to highly efficient waveguides formed from linear chains of defects doped with atoms or (quantum dots) can generate strong non-linear interactions which allow to implement both single and two qubit quantum gates. The simplicity of the gate switching mechanism, the experimental feasibility of fabricating two dimensional photonic crystal structures and integrability of this device with optoelectronics offers new interesting possibilities for optical quantum information processing networks.
... R. Lupacchini); L. Fortnow, Separating classes; B. Hart, The uncountable spectra of countable... more ... R. Lupacchini); L. Fortnow, Separating classes; B. Hart, The uncountable spectra of countable theories; G. Hjorth, Vaught conjecture on analytic sets; T. Jech, Stationary sets; C. Jockusch, Ramsey's theorem, computability, and second-order number theory; L. Lipshitz, The model ...
The classical theory of computation usually does not refer to physics. Pioneers such as Turing, C... more The classical theory of computation usually does not refer to physics. Pioneers such as Turing, Church, Post, and G��del managed to capture the correct classical theory by intuition alone and, as a result, it is often falsely assumed that its foundations are self-evident and purely abstract. They are not!
Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctu... more Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctuating around some average value that could be predicted by a classical theory, whereas all statistical properties of the fluctuations must be derived from a quantum theory. The character of the fluctuations depends on the quantum state of the field. Even in a vacuum, where the average value of the field is zero, its mean square value due to fluctuations is positive. This quantum noise associated with these fluctuations is inherent and cannot be removed no matter how carefully we get rid of various environmental disturbances and fluctuations. But even though the quantum noise is here to stay, we can still control and manipulate it.
A computation is a physical process. It may be performed by a piece of electronics or on an abacu... more A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines. 1 Physical Representation of Information Suppose you have n physical objects and each object has k distinguishable states. If you can access each object separately and put it into any of the k states then with very little effort you can prepare any of the N = k different configurations of the combined systems. Let us put k = 2 and refer to each object of this type as a physical bit. We label the two states of a physical bit as 0 and 1. Any collection of n physical bits can be prepared in N = 2 different configuratio...
12 1 2 1 2 , where |H⟩ and |V⟩ denote the horizontal and vertical polarization states, respective... more 12 1 2 1 2 , where |H⟩ and |V⟩ denote the horizontal and vertical polarization states, respectively, and the subscripts 1 and 2 denote the two output spatial modes. The entangled photon pairs are then collected and guided by two single-mode fibres to two independent transmitters equipped in the satellite. Both transmitters have a near-diffraction-limited far-field divergence of about 10 μrad. Under a pump power of 30 mW, the source distributes up to 5.9 × 10 6 entangled photon pairs per second. The photons are collected by the telescopes on two optical ground stations. For each one, the follow-up optics is installed on one of the rotating arms and rotates along with the telescope. As shown in Fig. 1c,
Device-independent quantum cryptography promises unprecedented security, but it is regarded as a ... more Device-independent quantum cryptography promises unprecedented security, but it is regarded as a theorist's dream and an experimentalist's nightmare. A new mathematical tool has now pushed its experimental demonstration much closer to reality.
Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of mod... more Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.
ABSTRACT Bell's inequality makes a seemingly insane scenario possible --- devices of unkn... more ABSTRACT Bell's inequality makes a seemingly insane scenario possible --- devices of unknown or dubious provenance, even those that are manufactured by our enemies, can be safely used for secret communication. And this is for real! All that is needed to implement such a bizarre form of cryptography is a loophole-free violation of Bell's inequalities. It is on the edge of being technologically feasible. I will provide a brief overview of quantum and post-quantum cryptography and describe how studies of entanglement and the foundations of quantum theory influenced the way we may soon protect information.
This is a brief description of how to protect quantum states from dissipation and decoherence tha... more This is a brief description of how to protect quantum states from dissipation and decoherence that arise due to uncontrolled interactions with the environment. We discuss recoherence and stabilization 0f quantum states based on two techniques known as "symmetrization" and "quantum error correction". We illustrate our considerations with the most popular quantum-optical model of the system-environment interaction, commonly used to describe spontaneous emission, and show the benefits of quantum error correction in this case.
A computation is a physical process. It may be performed by a piece of electronics or on an abacu... more A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (qua... more Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state ρABE. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this scenario as a unification of two standard scenarios: (i) key distillation (agreement) from classical correlations and (ii) key distillation from pure tripartite quantum states. Firstly, we obtain generalisations of fundamental results related to scenarios (i) and (ii), including upper bounds on the key rate, i.e., the number of key bits that can be extracted per copy of ρABE. Moreover, based on an embedding of classical distributions into quantum states, we are able to find new connections between protocols and quantities in the standard scenarios (i) and (ii). Secondly, we study specific properties of key distillation protocols. In particular, we show that every protocol that makes use of pre-shared key can be transformed into an equally efficient protocol which needs no pre-shared key. This result is of practical significance as it applies to quantum key distribution (QKD) protocols, but it also implies that the key rate cannot be locked with information on Eve's side. Finally, we exhibit an arbitrarily large separation between the key rate in the standard setting where Eve is equipped with quantum memory and the key rate in a setting where Eve is only given classical memory. This shows that assumptions on the nature of Eve's memory are important in order to determine the correct security threshold in QKD.
Quantum computers require technologies that offer both sufficient control over coherent quantum p... more Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We argue, that photons confined to photonic crystals, and in particular to highly efficient waveguides formed from linear chains of defects doped with atoms or (quantum dots) can generate strong non-linear interactions which allow to implement both single and two qubit quantum gates. The simplicity of the gate switching mechanism, the experimental feasibility of fabricating two dimensional photonic crystal structures and integrability of this device with optoelectronics offers new interesting possibilities for optical quantum information processing networks.
... R. Lupacchini); L. Fortnow, Separating classes; B. Hart, The uncountable spectra of countable... more ... R. Lupacchini); L. Fortnow, Separating classes; B. Hart, The uncountable spectra of countable theories; G. Hjorth, Vaught conjecture on analytic sets; T. Jech, Stationary sets; C. Jockusch, Ramsey's theorem, computability, and second-order number theory; L. Lipshitz, The model ...
The classical theory of computation usually does not refer to physics. Pioneers such as Turing, C... more The classical theory of computation usually does not refer to physics. Pioneers such as Turing, Church, Post, and G��del managed to capture the correct classical theory by intuition alone and, as a result, it is often falsely assumed that its foundations are self-evident and purely abstract. They are not!
Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctu... more Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctuating around some average value that could be predicted by a classical theory, whereas all statistical properties of the fluctuations must be derived from a quantum theory. The character of the fluctuations depends on the quantum state of the field. Even in a vacuum, where the average value of the field is zero, its mean square value due to fluctuations is positive. This quantum noise associated with these fluctuations is inherent and cannot be removed no matter how carefully we get rid of various environmental disturbances and fluctuations. But even though the quantum noise is here to stay, we can still control and manipulate it.
A computation is a physical process. It may be performed by a piece of electronics or on an abacu... more A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines. 1 Physical Representation of Information Suppose you have n physical objects and each object has k distinguishable states. If you can access each object separately and put it into any of the k states then with very little effort you can prepare any of the N = k different configurations of the combined systems. Let us put k = 2 and refer to each object of this type as a physical bit. We label the two states of a physical bit as 0 and 1. Any collection of n physical bits can be prepared in N = 2 different configuratio...
12 1 2 1 2 , where |H⟩ and |V⟩ denote the horizontal and vertical polarization states, respective... more 12 1 2 1 2 , where |H⟩ and |V⟩ denote the horizontal and vertical polarization states, respectively, and the subscripts 1 and 2 denote the two output spatial modes. The entangled photon pairs are then collected and guided by two single-mode fibres to two independent transmitters equipped in the satellite. Both transmitters have a near-diffraction-limited far-field divergence of about 10 μrad. Under a pump power of 30 mW, the source distributes up to 5.9 × 10 6 entangled photon pairs per second. The photons are collected by the telescopes on two optical ground stations. For each one, the follow-up optics is installed on one of the rotating arms and rotates along with the telescope. As shown in Fig. 1c,
Device-independent quantum cryptography promises unprecedented security, but it is regarded as a ... more Device-independent quantum cryptography promises unprecedented security, but it is regarded as a theorist's dream and an experimentalist's nightmare. A new mathematical tool has now pushed its experimental demonstration much closer to reality.
Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of mod... more Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.
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