We consider a topological Hamiltonian and establish a correspondence between its eigenstates and ... more We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1], known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state (GS) of the model can be related to the optimal strategy of the causal order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal order game, corresponding quantum many-body model undergoes a second-order quantum phase transition (QPT). The correspondence equally holds even when we generalize the game for a higher number of parties. H(θ) = −2 cos θ 2 ∑ i=1 σ i z σ i+2 z − sin θ 4 ∑ i=1 σ i z σ i+1 x σ i+2 z , (1) where σ k i are the Pauli matrices at site k (i ∈ x, y, z) and we consider periodic boundary conditions (PBC). It is apparent that for this small system size the model can be diagonalized instantly. However, one can note that even for any arbitrary N, the model can be exactly diagonalized by first applying certain non-local unitary transformation on pair of sites and then
Anindita Bera, Filip A. Wudarski, 3 Gniewomir Sarbicki, and Dariusz Chruściński Institute of Phys... more Anindita Bera, Filip A. Wudarski, 3 Gniewomir Sarbicki, and Dariusz Chruściński Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5/7, 87–100 Toruń, Poland Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, CA 94035, USA USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043, USA Two classes of Bell diagonal indecomposable entanglement witnesses in C ⊗ C are considered. Within the first class, we find a generalization of the well-known Choi witness from C ⊗ C, while the second one contains the reduction map. Interestingly, contrary to C ⊗C case, the generalized Choi witnesses are no longer optimal. We perform an optimization procedure of finding spanning vectors, that eventually gives rise to optimal witnesses. Operators from the second class turn out to be optimal, however, without the spanning property. This analys...
We investigate the effect of a unidirectional quenched random field on the anisotropic quantum sp... more We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 XY model, which magnetizes spontaneously in the absence of the random field. We adopt mean-field approach to show that spontaneous magnetization persists even in the presence of this random field but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained by analytical calculations within perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of the magnetization in presence of the disorder field provided we apply an additional constant field in the XY plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the XY spin system with arbitrary fixed quantum spin angular momentum.
We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external... more We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or/and annealed disorder. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales - the time scale associated with the equilibriation of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We observe in particular that when interaction and field terms are respectively quenched and annealed, critical temperature for the system to magnetize in the direction parallel to the applied field does not depend on any of the disorders. Further, an a...
We consider classical spin models of two- and three-dimensional spins with continuous symmetry an... more We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show, by perturbative calculations and numerical simulations, that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature, at which the system starts magnetizing, as well as the magnetization at low and high temperature limits, in presence of disorder, are estimated. Moreover, we treat the SO(n) n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XY spin model in the presence ...
We propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz cons... more We propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz constants of the corresponding position and momentum probability distributions. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.
Anindita Bera, 2 Debraj Rakshit, Maciej Lewenstein, 4 Aditi Sen(De), Ujjwal Sen, and Jan Wehr Dep... more Anindita Bera, 2 Debraj Rakshit, Maciej Lewenstein, 4 Aditi Sen(De), Ujjwal Sen, and Jan Wehr Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700 009, India Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India ICFO-Institut de Ciències Fotòniques, Av. C.F. Gauss 3, 08860 Castelldefels (Barcelona), Spain ICREA-Institució Catalana de Recerca i Estudis Avancats, Lluis Companys 23, 08010 Barcelona, Spain Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089, USA (Dated: November 7, 2018)
We consider a topological Hamiltonian and establish a correspondence between its eigenstates and ... more We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1], known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state of the model can be related to the optimal strategy of the causal order game. Along with this, we show that a correspondence between the considered topological quantum Hamiltonian and the causal order game can also be made by relating the behavior of topological order parameters characterizing different phases of the model with the different regions of the causal order ga...
Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We pr... more Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.
Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C. Hiesmayr, and Daniel McNulty 5 1 Scho... more Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C. Hiesmayr, and Daniel McNulty 5 1 School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro Yuseong-gu, Daejeon 34141 Republic of Korea, 2 Institute of Physics, Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University, Grudzia̧dzka 5/7, 87–100 Toruń, Poland, University of Vienna, Faculty of Physics, Währinger Straße 17, 1090 Vienna, Austria, Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland, Department of Mathematics, Aberystwyth University, Aberystwyth, Wales, U.K.
We propose a trade-off between the Lipschitz constants of the position and momentum probability d... more We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck’s constant.
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via ... more In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.
Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We pr... more Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.
We study the growth of genuine multipartite entanglement in random unitary circuit models consist... more We study the growth of genuine multipartite entanglement in random unitary circuit models consisting of both short-and long-range unitaries. We observe that circuits with short-range unitaries are optimal for generating large global entanglement, which, interestingly, is found to be close to the global entanglement in random matrix product states with moderately high bond dimension. Furthermore, the behavior of multipartite entanglement can be related to other global properties of the system, viz. the delocalization of the many-body wavefunctions. Moreover, we show that the circuit can sustain a finite amount of genuine multipartite entanglement even when it is monitored through weak measurements.
Complete measurements, while providing maximal information gain, results in destruction of the sh... more Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.
We introduce a probabilistic version of the one-shot quantum dense coding protocol in both twoand... more We introduce a probabilistic version of the one-shot quantum dense coding protocol in both twoand multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of shared states between two, three, and more qubits, and two qutrits. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.
We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on th... more We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement − order-from-disorder − is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.
We propose a trade-off between the Lipschitz constants of the position and momentum probability d... more We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant. A mapping f : D → C from domain D (⊆ R n ) into the set of complex numbers C is said to be Lipschitz
We consider a topological Hamiltonian and establish a correspondence between its eigenstates and ... more We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1], known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state (GS) of the model can be related to the optimal strategy of the causal order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal order game, corresponding quantum many-body model undergoes a second-order quantum phase transition (QPT). The correspondence equally holds even when we generalize the game for a higher number of parties. H(θ) = −2 cos θ 2 ∑ i=1 σ i z σ i+2 z − sin θ 4 ∑ i=1 σ i z σ i+1 x σ i+2 z , (1) where σ k i are the Pauli matrices at site k (i ∈ x, y, z) and we consider periodic boundary conditions (PBC). It is apparent that for this small system size the model can be diagonalized instantly. However, one can note that even for any arbitrary N, the model can be exactly diagonalized by first applying certain non-local unitary transformation on pair of sites and then
Anindita Bera, Filip A. Wudarski, 3 Gniewomir Sarbicki, and Dariusz Chruściński Institute of Phys... more Anindita Bera, Filip A. Wudarski, 3 Gniewomir Sarbicki, and Dariusz Chruściński Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5/7, 87–100 Toruń, Poland Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, CA 94035, USA USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043, USA Two classes of Bell diagonal indecomposable entanglement witnesses in C ⊗ C are considered. Within the first class, we find a generalization of the well-known Choi witness from C ⊗ C, while the second one contains the reduction map. Interestingly, contrary to C ⊗C case, the generalized Choi witnesses are no longer optimal. We perform an optimization procedure of finding spanning vectors, that eventually gives rise to optimal witnesses. Operators from the second class turn out to be optimal, however, without the spanning property. This analys...
We investigate the effect of a unidirectional quenched random field on the anisotropic quantum sp... more We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 XY model, which magnetizes spontaneously in the absence of the random field. We adopt mean-field approach to show that spontaneous magnetization persists even in the presence of this random field but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained by analytical calculations within perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of the magnetization in presence of the disorder field provided we apply an additional constant field in the XY plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the XY spin system with arbitrary fixed quantum spin angular momentum.
We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external... more We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or/and annealed disorder. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales - the time scale associated with the equilibriation of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We observe in particular that when interaction and field terms are respectively quenched and annealed, critical temperature for the system to magnetize in the direction parallel to the applied field does not depend on any of the disorders. Further, an a...
We consider classical spin models of two- and three-dimensional spins with continuous symmetry an... more We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show, by perturbative calculations and numerical simulations, that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature, at which the system starts magnetizing, as well as the magnetization at low and high temperature limits, in presence of disorder, are estimated. Moreover, we treat the SO(n) n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XY spin model in the presence ...
We propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz cons... more We propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz constants of the corresponding position and momentum probability distributions. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.
Anindita Bera, 2 Debraj Rakshit, Maciej Lewenstein, 4 Aditi Sen(De), Ujjwal Sen, and Jan Wehr Dep... more Anindita Bera, 2 Debraj Rakshit, Maciej Lewenstein, 4 Aditi Sen(De), Ujjwal Sen, and Jan Wehr Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700 009, India Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India ICFO-Institut de Ciències Fotòniques, Av. C.F. Gauss 3, 08860 Castelldefels (Barcelona), Spain ICREA-Institució Catalana de Recerca i Estudis Avancats, Lluis Companys 23, 08010 Barcelona, Spain Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089, USA (Dated: November 7, 2018)
We consider a topological Hamiltonian and establish a correspondence between its eigenstates and ... more We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1], known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state of the model can be related to the optimal strategy of the causal order game. Along with this, we show that a correspondence between the considered topological quantum Hamiltonian and the causal order game can also be made by relating the behavior of topological order parameters characterizing different phases of the model with the different regions of the causal order ga...
Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We pr... more Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.
Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C. Hiesmayr, and Daniel McNulty 5 1 Scho... more Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C. Hiesmayr, and Daniel McNulty 5 1 School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro Yuseong-gu, Daejeon 34141 Republic of Korea, 2 Institute of Physics, Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University, Grudzia̧dzka 5/7, 87–100 Toruń, Poland, University of Vienna, Faculty of Physics, Währinger Straße 17, 1090 Vienna, Austria, Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland, Department of Mathematics, Aberystwyth University, Aberystwyth, Wales, U.K.
We propose a trade-off between the Lipschitz constants of the position and momentum probability d... more We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck’s constant.
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via ... more In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.
Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We pr... more Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.
We study the growth of genuine multipartite entanglement in random unitary circuit models consist... more We study the growth of genuine multipartite entanglement in random unitary circuit models consisting of both short-and long-range unitaries. We observe that circuits with short-range unitaries are optimal for generating large global entanglement, which, interestingly, is found to be close to the global entanglement in random matrix product states with moderately high bond dimension. Furthermore, the behavior of multipartite entanglement can be related to other global properties of the system, viz. the delocalization of the many-body wavefunctions. Moreover, we show that the circuit can sustain a finite amount of genuine multipartite entanglement even when it is monitored through weak measurements.
Complete measurements, while providing maximal information gain, results in destruction of the sh... more Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.
We introduce a probabilistic version of the one-shot quantum dense coding protocol in both twoand... more We introduce a probabilistic version of the one-shot quantum dense coding protocol in both twoand multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of shared states between two, three, and more qubits, and two qutrits. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.
We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on th... more We investigate bipartite entanglement in random quantum XY models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement − order-from-disorder − is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.
We propose a trade-off between the Lipschitz constants of the position and momentum probability d... more We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is in general independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant. A mapping f : D → C from domain D (⊆ R n ) into the set of complex numbers C is said to be Lipschitz
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