We discuss quantum information processing machines. We start with single purpose machines that ei... more We discuss quantum information processing machines. We start with single purpose machines that either redistribute quantum information or identify quantum states. We then move on to machines that can perform a number of functions, with the function they perform being determined by a program, which is itself a quantum state. Examples of both deterministic and probabilistic programmable machines are given, and we conclude with a discussion of the utility of quantum programs.
We present a network consisting of quantum gates which produces two imperfect copies of an arbitr... more We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network.
Quantum and Semiclassical Optics: Journal of the European Optical Society Part B
We focus our attention on the problem of reconstruction of density operators of quantum states fr... more We focus our attention on the problem of reconstruction of density operators of quantum states from propensities, i.e. generalized quasiprobability density distributions obtained by quantum filtering. We consider propensities obtained by filtering with pure Gaussian as well as non-Gaussian states and we present two examples: when the filter is in a squeezed coherent state and in a Fock state, respectively. We also show that even in the case of filtering with statistical mixtures a complete reconstruction of a density operator of the measured quantum state can be performed.
Quantum Optics: Journal of the European Optical Society Part B
The authors have investigated the spectrum of the emitted light by a single atom interacting with... more The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.
In this paper we study the time evolution of the atomic inversion of the two-level atom which is ... more In this paper we study the time evolution of the atomic inversion of the two-level atom which is coupled to the q analogue of a single mode of the bosonic field. The q field under consideration is supposed to be prepared initially in the q analogue of Glauber's coherent state. We find that q deformation of Heisenberg algebra may correspond to some effective nonlinear interaction of the cavity mode.
We review our recent work on the universal (i.e. input state independent) optimal quantum copying... more We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying "machine" (transformation) which produces N + 1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.
The nature of the quantum fluctuations in a light field created by the superposition of coherent ... more The nature of the quantum fluctuations in a light field created by the superposition of coherent fields is investigated. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the one-dimensional superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.
Usually it is assumed that quantum dense coding is due to quantum entanglement between two partie... more Usually it is assumed that quantum dense coding is due to quantum entanglement between two parties. We show that this phenomenon has its origin in correlations between two parties rather than simply in entanglement. In order to justify our argument we considered that Alice has a qubit in the state ̺ = 1 2 1 1 + n • σ and we evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice and (2) in the case when he utilizes the whole potential of the dense coding, that is, he performs the measurement on the received particle and the particle he had prior to the communication. We also present a simple classical scenario which might serve as a prototype of the dense coding. We generalize our results also for qudits.
Four basis vectors of the Hilbert space of two qubits have the property that if three of them are... more Four basis vectors of the Hilbert space of two qubits have the property that if three of them are product states, then the fourth one has to be a product state as well. We address the following situation: Consider a set of orthogonal vectors, each exhibiting a certain degree of entanglement. What is the bound on entanglement of the rest of the basis vectors to form a complete orthonormal basis? Specifically, we present an orthonormal basis, the Xi basis in the Hilbert space of two qubits, with one product state and three equally entangled states. The maximum of the so available entanglement is quantified. A close-to-optimal protocol is presented for entanglement purification via entanglement swapping of two-qubit states. It is based on a suitably chosen nonmaximally entangled basis and carried out in a single step without any ancillas. A similar application of the Xi basis is examined. In this latter case, all the involved entangled states have different and nonorthogonal Schmidt decompositions and, except for some possibly resulting states, none of them are maximally entangled. Entanglement of single pair purification is not conserved on average in this case.
Squeezed States and Uncertainty Relations, Feb 1, 1992
We investigate the nature of the quantum fluctuations in a light field created by the superpositi... more We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the one-dimensional superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states. which appears as a consequence of quantum interference between coherent states. Light squeezing (for recent reviews see [2] as well as topical issues of JOSA B [3] and J. Mod. Opt. [4]) remains a central topic in quantum optics. Generation of squeezed light has been reported by various groups [5-11] and offers new opportunities for the utilization of light with reduced quadrature noise in interferometry, fiber optics communications and high-precision experiments. Most studies of squeezed states have concentrated on those states generated by quadratic field interaction (e.g. parametric amplification). Recently it has been shown by W6dkiewicz and eoworkers [12] that a superposition of two number states (for instance, the vacuum state and the one-or two-photon states) of a single mode electromagnetic field exhibits interesting non-classical properties. In particular, squeezing of the variances of the quadrature operators can be seen (although not necessarily of the quadratic, minimum uncertainty state quality).
We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-reson... more We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).
Zeitschrift Fur Physik D Atoms Molecules and Clusters, 1990
We study exactly solvable Dicke-like model describing a system of spatially distributed two-level... more We study exactly solvable Dicke-like model describing a system of spatially distributed two-level atoms coupled to a single mode cavity field. We study the model in one excitation sub-space, when the field is supposed to be initially in the vacuum state and just one atom of the atomic sample is excited. We show that depending on the particular spatial distribution
A quantum processor is a device with a data register and a program register. The input to the pro... more A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices. We generalize the concept of quantum programmable processors and we propose
We discuss quantum information processing machines. We start with single purpose machines that ei... more We discuss quantum information processing machines. We start with single purpose machines that either redistribute quantum information or identify quantum states. We then move on to machines that can perform a number of functions, with the function they perform being determined by a program, which is itself a quantum state. Examples of both deterministic and probabilistic programmable machines are given, and we conclude with a discussion of the utility of quantum programs.
We present a network consisting of quantum gates which produces two imperfect copies of an arbitr... more We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network.
Quantum and Semiclassical Optics: Journal of the European Optical Society Part B
We focus our attention on the problem of reconstruction of density operators of quantum states fr... more We focus our attention on the problem of reconstruction of density operators of quantum states from propensities, i.e. generalized quasiprobability density distributions obtained by quantum filtering. We consider propensities obtained by filtering with pure Gaussian as well as non-Gaussian states and we present two examples: when the filter is in a squeezed coherent state and in a Fock state, respectively. We also show that even in the case of filtering with statistical mixtures a complete reconstruction of a density operator of the measured quantum state can be performed.
Quantum Optics: Journal of the European Optical Society Part B
The authors have investigated the spectrum of the emitted light by a single atom interacting with... more The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.
In this paper we study the time evolution of the atomic inversion of the two-level atom which is ... more In this paper we study the time evolution of the atomic inversion of the two-level atom which is coupled to the q analogue of a single mode of the bosonic field. The q field under consideration is supposed to be prepared initially in the q analogue of Glauber's coherent state. We find that q deformation of Heisenberg algebra may correspond to some effective nonlinear interaction of the cavity mode.
We review our recent work on the universal (i.e. input state independent) optimal quantum copying... more We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying "machine" (transformation) which produces N + 1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.
The nature of the quantum fluctuations in a light field created by the superposition of coherent ... more The nature of the quantum fluctuations in a light field created by the superposition of coherent fields is investigated. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the one-dimensional superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.
Usually it is assumed that quantum dense coding is due to quantum entanglement between two partie... more Usually it is assumed that quantum dense coding is due to quantum entanglement between two parties. We show that this phenomenon has its origin in correlations between two parties rather than simply in entanglement. In order to justify our argument we considered that Alice has a qubit in the state ̺ = 1 2 1 1 + n • σ and we evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice and (2) in the case when he utilizes the whole potential of the dense coding, that is, he performs the measurement on the received particle and the particle he had prior to the communication. We also present a simple classical scenario which might serve as a prototype of the dense coding. We generalize our results also for qudits.
Four basis vectors of the Hilbert space of two qubits have the property that if three of them are... more Four basis vectors of the Hilbert space of two qubits have the property that if three of them are product states, then the fourth one has to be a product state as well. We address the following situation: Consider a set of orthogonal vectors, each exhibiting a certain degree of entanglement. What is the bound on entanglement of the rest of the basis vectors to form a complete orthonormal basis? Specifically, we present an orthonormal basis, the Xi basis in the Hilbert space of two qubits, with one product state and three equally entangled states. The maximum of the so available entanglement is quantified. A close-to-optimal protocol is presented for entanglement purification via entanglement swapping of two-qubit states. It is based on a suitably chosen nonmaximally entangled basis and carried out in a single step without any ancillas. A similar application of the Xi basis is examined. In this latter case, all the involved entangled states have different and nonorthogonal Schmidt decompositions and, except for some possibly resulting states, none of them are maximally entangled. Entanglement of single pair purification is not conserved on average in this case.
Squeezed States and Uncertainty Relations, Feb 1, 1992
We investigate the nature of the quantum fluctuations in a light field created by the superpositi... more We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the one-dimensional superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states. which appears as a consequence of quantum interference between coherent states. Light squeezing (for recent reviews see [2] as well as topical issues of JOSA B [3] and J. Mod. Opt. [4]) remains a central topic in quantum optics. Generation of squeezed light has been reported by various groups [5-11] and offers new opportunities for the utilization of light with reduced quadrature noise in interferometry, fiber optics communications and high-precision experiments. Most studies of squeezed states have concentrated on those states generated by quadratic field interaction (e.g. parametric amplification). Recently it has been shown by W6dkiewicz and eoworkers [12] that a superposition of two number states (for instance, the vacuum state and the one-or two-photon states) of a single mode electromagnetic field exhibits interesting non-classical properties. In particular, squeezing of the variances of the quadrature operators can be seen (although not necessarily of the quadratic, minimum uncertainty state quality).
We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-reson... more We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).
Zeitschrift Fur Physik D Atoms Molecules and Clusters, 1990
We study exactly solvable Dicke-like model describing a system of spatially distributed two-level... more We study exactly solvable Dicke-like model describing a system of spatially distributed two-level atoms coupled to a single mode cavity field. We study the model in one excitation sub-space, when the field is supposed to be initially in the vacuum state and just one atom of the atomic sample is excited. We show that depending on the particular spatial distribution
A quantum processor is a device with a data register and a program register. The input to the pro... more A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices. We generalize the concept of quantum programmable processors and we propose
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Papers by Vladimir Buzek