This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be ... more This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be substituted by a new work.
We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could ... more We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could also be unknown, to a Bell state. The setup involves two linear optical circuits processing the individual photons and a parity gate working with weak cross-Kerr nonlinearity. By the photon number resolving detection on one of the output quantum bus or communication beams, the setup will realize a near deterministic transformation to a Bell state for every entangling attempt. With the simple threshold detectors, on the other hand, the system can still reach a considerable success probability of 0.5 per try. The decoherence effect caused by photon absorption losses in the operation is also discussed.
There are presently two models for quantum walks on graphs. The "coined" walk uses disc... more There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for a quantum walk is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. No quantum coin is introduced. This type of walk allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Walks on the line and cycle are discussed in some detail, and a probability current for these walks is introduced. The relation to the coined quantum walk is also discussed. The paper concludes by showing how to define these walks for a general g...
We suggest a quantum measurement model in an ion trap which specifies the probability distributio... more We suggest a quantum measurement model in an ion trap which specifies the probability distribution of two, distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter which, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question to what extend the Bell inequality can be considered as a measure of entanglement.
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states ... more Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, |ψ_1 >, ..., |ψ_N >, for distinguishing |ψ_1 > from the set |ψ_2 >, ..., |ψ_N > and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased f...
We present a quantum repeater protocol that generates the elementary segments of entangled photon... more We present a quantum repeater protocol that generates the elementary segments of entangled photons through the communication of qubus in coherent states. The input photons at the repeater stations can be in arbitrary states to save the local state preparation time for the operations. The flexibility of the scheme accelerates the generation of the elementary segments (close to the exact Bell states) to a high rate for practical quantum communications. The entanglement connection to long distances is simplified and sped up, possibly realizing an entangled pair of high quality within the time in the order of that for classical communication between two far-away locations.
It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum... more It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of the different states, we shall only discriminate between two subsets of them. In particular, for the case of three non-orthogonal states, we show that the optimal strategy to distinguish between a set containing one of the states from the set containing the other two has a higher success rate than if we wish to discriminate among all three states. Somewhat surprisingly, for unambiguous discrimination the subsets need not be linearly independent. A fully analytical solution is presented, and we also show how to construct generalized interferometers (multiports) that provide an optical implementation of the optimal strategy.
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time ... more There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walks operate with continuous time. Here a third model for quatum walks is proposed, which is based on an analogy to optical interferometers. It is a discretetime model, and the unitary operator that advances the walk one step depnds only on the local structure of the graph on which the walk is taking place. This type of walk also allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Several examples are discussed.
We discuss a state discriminator that unambiguously distinguishes between two quantum registers p... more We discuss a state discriminator that unambiguously distinguishes between two quantum registers prepared with multiple copies of two unknown qubits. This device achieves the optimal performance by von Neumann measurement and general POVM in different ranges of the input preparation probabilities, respectively, and in the limit of very large program registers the optimal measurement reduces to only von Neumann measurements.
2021 IEEE International Conference on Quantum Computing and Engineering (QCE)
Quantum information processing using linear optics is challenging due to the limited set of deter... more Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillas, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50% we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprised of single photon detectors and beam splitters with input state-dependent parameters that achieves optimal discrimination in the Bell-like case.
We present wave-particle duality relations involving the relative entropy coherence measure, whic... more We present wave-particle duality relations involving the relative entropy coherence measure, which plays a prominent role in the resource theory of coherence. The main input in these relations is an entropic bound for the which-way information, which we derive in this letter. We show that this latter crucially depends on the choice of the measurement strategy to obtain the path information. In particular, we present results for two strategies: zero-error identification of the path-detector states, which never produces an error but sometimes fails to return a conclusive answer, and a mixed strategy where both errors and failure are allowed.
I also wish to draw your attention on the Nutrients website to our Editorial Board and also to th... more I also wish to draw your attention on the Nutrients website to our Editorial Board and also to the guest editors of our expanding list of special issues who have devoted their time and expertise to achieving rapid growth in the quantity and quality of published manuscripts. My special thanks also to Associate Editor, Jon Buckley, and members of the editorial office for their dedication to the journal.
We show that the protocol known as quantum state separation can be used to transfer information b... more We show that the protocol known as quantum state separation can be used to transfer information between the phase and path of a particle in an interferometer. When applied to a quantum eraser, this allows us to erase some, but not all, of the path information. We can control how much path information we wish to erase.
Laser oscillation on transitions of Al II was investigated in a large diameter hollow cathode dis... more Laser oscillation on transitions of Al II was investigated in a large diameter hollow cathode discharge where Al vapour was produced by cathode sputtering. The special internal anode system used considerably increased the tube voltage and resulted low threshold currents.
We analyze the effects of the injected atomic coherence in the Jaynes-Cummings model. Various con... more We analyze the effects of the injected atomic coherence in the Jaynes-Cummings model. Various conditions for squeezed state generation are studied. Also, for short times, it is possible to distinguish regions where a squeezed state builds up and where it does not.
The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedu... more The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedures for a charged particle embedded simultaneously in a plane-wave radiation field and in a uniform magnetic field which is directed parallel to the direction of propagation of the plane wave. Two cases of the solutions are considered: (i) the radiation field is a classical external plane wave and (ii) it is a quantized field. The connection with less explicit or more specific solutions of this problem known previously is established and possible applications are discussed.
A nonrelativistic theory of charged-particle scattering by a background potential V(r} in the sim... more A nonrelativistic theory of charged-particle scattering by a background potential V(r} in the simultaneous presence of a magnetic and a laser field is developed. The particle motion in the magnetic and laser field in dipole approximation is treated exactly. Transitions between exact quantum-mechanical states of the charged particle are considered to lowestorder Born approximation in V(r). Conservation laws and selection rules for the scattering are derived for the case of laser light circularly polarized in the plane perpendicular to the magnetic field direction. It is shown that nonlinear bremsstrahlung may occur accompanied by a corresponding change of the electron's angular momentum component along the magnetic field axis. Transition amplitudes for these cases are presented in closed form and their electric and magnetic field dependences are discussed in the limiting cases of weak and strong magnetic and laser fields. The connection of this approach to previous work is established.
This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be ... more This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be substituted by a new work.
We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could ... more We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could also be unknown, to a Bell state. The setup involves two linear optical circuits processing the individual photons and a parity gate working with weak cross-Kerr nonlinearity. By the photon number resolving detection on one of the output quantum bus or communication beams, the setup will realize a near deterministic transformation to a Bell state for every entangling attempt. With the simple threshold detectors, on the other hand, the system can still reach a considerable success probability of 0.5 per try. The decoherence effect caused by photon absorption losses in the operation is also discussed.
There are presently two models for quantum walks on graphs. The "coined" walk uses disc... more There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for a quantum walk is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. No quantum coin is introduced. This type of walk allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Walks on the line and cycle are discussed in some detail, and a probability current for these walks is introduced. The relation to the coined quantum walk is also discussed. The paper concludes by showing how to define these walks for a general g...
We suggest a quantum measurement model in an ion trap which specifies the probability distributio... more We suggest a quantum measurement model in an ion trap which specifies the probability distribution of two, distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter which, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question to what extend the Bell inequality can be considered as a measure of entanglement.
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states ... more Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, |ψ_1 >, ..., |ψ_N >, for distinguishing |ψ_1 > from the set |ψ_2 >, ..., |ψ_N > and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased f...
We present a quantum repeater protocol that generates the elementary segments of entangled photon... more We present a quantum repeater protocol that generates the elementary segments of entangled photons through the communication of qubus in coherent states. The input photons at the repeater stations can be in arbitrary states to save the local state preparation time for the operations. The flexibility of the scheme accelerates the generation of the elementary segments (close to the exact Bell states) to a high rate for practical quantum communications. The entanglement connection to long distances is simplified and sped up, possibly realizing an entangled pair of high quality within the time in the order of that for classical communication between two far-away locations.
It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum... more It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of the different states, we shall only discriminate between two subsets of them. In particular, for the case of three non-orthogonal states, we show that the optimal strategy to distinguish between a set containing one of the states from the set containing the other two has a higher success rate than if we wish to discriminate among all three states. Somewhat surprisingly, for unambiguous discrimination the subsets need not be linearly independent. A fully analytical solution is presented, and we also show how to construct generalized interferometers (multiports) that provide an optical implementation of the optimal strategy.
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time ... more There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walks operate with continuous time. Here a third model for quatum walks is proposed, which is based on an analogy to optical interferometers. It is a discretetime model, and the unitary operator that advances the walk one step depnds only on the local structure of the graph on which the walk is taking place. This type of walk also allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Several examples are discussed.
We discuss a state discriminator that unambiguously distinguishes between two quantum registers p... more We discuss a state discriminator that unambiguously distinguishes between two quantum registers prepared with multiple copies of two unknown qubits. This device achieves the optimal performance by von Neumann measurement and general POVM in different ranges of the input preparation probabilities, respectively, and in the limit of very large program registers the optimal measurement reduces to only von Neumann measurements.
2021 IEEE International Conference on Quantum Computing and Engineering (QCE)
Quantum information processing using linear optics is challenging due to the limited set of deter... more Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillas, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50% we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprised of single photon detectors and beam splitters with input state-dependent parameters that achieves optimal discrimination in the Bell-like case.
We present wave-particle duality relations involving the relative entropy coherence measure, whic... more We present wave-particle duality relations involving the relative entropy coherence measure, which plays a prominent role in the resource theory of coherence. The main input in these relations is an entropic bound for the which-way information, which we derive in this letter. We show that this latter crucially depends on the choice of the measurement strategy to obtain the path information. In particular, we present results for two strategies: zero-error identification of the path-detector states, which never produces an error but sometimes fails to return a conclusive answer, and a mixed strategy where both errors and failure are allowed.
I also wish to draw your attention on the Nutrients website to our Editorial Board and also to th... more I also wish to draw your attention on the Nutrients website to our Editorial Board and also to the guest editors of our expanding list of special issues who have devoted their time and expertise to achieving rapid growth in the quantity and quality of published manuscripts. My special thanks also to Associate Editor, Jon Buckley, and members of the editorial office for their dedication to the journal.
We show that the protocol known as quantum state separation can be used to transfer information b... more We show that the protocol known as quantum state separation can be used to transfer information between the phase and path of a particle in an interferometer. When applied to a quantum eraser, this allows us to erase some, but not all, of the path information. We can control how much path information we wish to erase.
Laser oscillation on transitions of Al II was investigated in a large diameter hollow cathode dis... more Laser oscillation on transitions of Al II was investigated in a large diameter hollow cathode discharge where Al vapour was produced by cathode sputtering. The special internal anode system used considerably increased the tube voltage and resulted low threshold currents.
We analyze the effects of the injected atomic coherence in the Jaynes-Cummings model. Various con... more We analyze the effects of the injected atomic coherence in the Jaynes-Cummings model. Various conditions for squeezed state generation are studied. Also, for short times, it is possible to distinguish regions where a squeezed state builds up and where it does not.
The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedu... more The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedures for a charged particle embedded simultaneously in a plane-wave radiation field and in a uniform magnetic field which is directed parallel to the direction of propagation of the plane wave. Two cases of the solutions are considered: (i) the radiation field is a classical external plane wave and (ii) it is a quantized field. The connection with less explicit or more specific solutions of this problem known previously is established and possible applications are discussed.
A nonrelativistic theory of charged-particle scattering by a background potential V(r} in the sim... more A nonrelativistic theory of charged-particle scattering by a background potential V(r} in the simultaneous presence of a magnetic and a laser field is developed. The particle motion in the magnetic and laser field in dipole approximation is treated exactly. Transitions between exact quantum-mechanical states of the charged particle are considered to lowestorder Born approximation in V(r). Conservation laws and selection rules for the scattering are derived for the case of laser light circularly polarized in the plane perpendicular to the magnetic field direction. It is shown that nonlinear bremsstrahlung may occur accompanied by a corresponding change of the electron's angular momentum component along the magnetic field axis. Transition amplitudes for these cases are presented in closed form and their electric and magnetic field dependences are discussed in the limiting cases of weak and strong magnetic and laser fields. The connection of this approach to previous work is established.
Uploads
Papers by Janos Bergou