We explore the possibility of using "weak measurements" without "weak value" for quantum state es... more We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue and recycle the state, unlike for the case of projective measurements. We use this property of weak measurements and design schemes for quantum state estimation for qubits and for Gaussian states. We show, via numerical simulations, that under certain circumstances, our method can outperform the estimation by projective measurements. It turns out that ensemble size plays an important role and the scheme based on recycling works better for small ensembles. A. Von Neumann's measurement model for discrete basis Consider the measurement of an observable A of a quantum system with eigenvectors {|a j } and eigenvalues {a j }, j = 1 • • • n. Imagine an apparatus with continuous pointer positions described by a variable q and its
We introduce local filters as a means to detect the entanglement of bound entangled states which ... more We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurementbased implementation of these filters for 2 ⊗ 2 and 3 ⊗ 3 systems. This provides us with a physical mechanism to implement such local filters.
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and ce... more Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent time evolution and do not explicitly reconstruct the full time-dependent Hamiltonian or interrupt evolution for tomography. Here, we experimentally demonstrate that an a priori unknown, time-dependent Hamiltonian can be reconstructed from continuous weak measurements concurrent with coherent time evolution in a system of two superconducting transmons coupled by a flux-tunable coupler. In contrast to previous work, our technique does not require interruptions, which would distort the recovered Hamiltonian. We introduce an algorithm which recovers the Hamiltonian and density matrix from an incomplete set of continuous measurements and demonstrate that it reliably extracts amplitudes of a variety of single qubit and entangling two qubit Hamiltonians. We further demonstrate how this technique reveals deviations from a theoretical control Hamiltonian which would otherwise be missed by conventional techniques. Our work opens up novel applications for continuous weak measurements, such as studying non-idealities in gates, certifying analog quantum simulators, and performing quantum metrology.
The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", i... more The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissociated from a property of the object, identified with the "grin" of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g., two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit-coupling-like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a so-called confused Cheshire cat. We devise a gedanken experiment in which such a "confusion" can be successfully dissociated from the system, and we find that the dissociation helps in the amplification of signals.
The trade-off between robustness and tunability is a central challenge in the pursuit of quantum ... more The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ and SWAP gates with good estimated fidelities. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate, also with a competitive fidelity. Our protocol applies to multiple fixed-frequency high-coherence platforms, providing a collection of interactions for high-performance quantum information processing. It also establishes the potential of the Floquet framework as a tool for exploring quantum electrodynamics and optimal control.
Based on the statistical concept of the median, we propose a quantum uncertainty relation between... more Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography.
The quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissocia... more The quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissociated from a property of the object, identified with the "grin" of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g. two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit coupling-like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a "confused Cheshire cat". We devise a gedanken experiment in which such a "confusion" can be successfully dissociated from the system, and we find that the dissociation helps in amplification of signals.
We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and... more We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is achieved in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions and bosons.
We experimentally construct a novel three-qubit entangled W-superposition (WW) state on an NMR qu... more We experimentally construct a novel three-qubit entangled W-superposition (WW) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the WW state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party WW state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the WW state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the WW state is interconvertible with the GHZ state, it stores entanglement very differently.
We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and... more We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is achieved in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions and bosons.
We explore the possibility of using "weak" measurements to carry out quantum state tomography via... more We explore the possibility of using "weak" measurements to carry out quantum state tomography via numerical simulations. Given a fixed number of copies of identically prepared states of a qubit, we perform state tomography using weak as well as projective measurements. Due to the collapse of the state after measurement, we cannot reuse the state after a projective measurement. If the coupling strength between the quantum system and the measurement device is made weaker, the disturbance caused to the state can be lowered. This then allows us to reuse the same member of the ensemble for further measurements and thus extract more information from the system. However, this happens at the cost of getting imprecise information from the first measurement. We implement this scheme for a single qubit and show that under certain circumstances, it can outperform the projective measurement-based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths, and different ensemble sizes.
The quantum Cheshire Cat is a mysterious phenomenon that temporarily strips a system - a "ca... more The quantum Cheshire Cat is a mysterious phenomenon that temporarily strips a system - a "cat"- of its property - its "grin". A corollary of this effect is the decoupling of two properties of the same system, which we call the grin and the snarl. This can in principle be realized by detecting two components of polarization of a photon in two different arms of an interferometer. We introduce a mechanism by which we can interchange the positions of these two properties. By doing this we uncover a phenomenon that decouples the grin and the snarl, and puts them in their place even before they encounter the mechanism.
Based on the statistical concept of the median, we propose a quantum uncertainty relation between... more Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies in...
Quantum Chesire Cat is a counterintuitive phenomenon that provides a new window into the nature o... more Quantum Chesire Cat is a counterintuitive phenomenon that provides a new window into the nature of the quantum systems in relation to multiple degrees of freedom associated with a single physical entity. Under suitable pre and postselections, a photon (the cat) can be decoupled from its circular polarization (its grin). In this paper, we explore whether the grin without the cat can be teleported to a distant location. This will be a totally disembodied teleportation protocol. Based on the original Quantum Chesire Cat setup, we design a protocol where the circular polarization is successfully teleported between two spatially separated parties even when the photon is not physically present with them. The process raises questions in our understanding about properties of quantum system. In particular it shows that question like ``whose polarization is it'' can prove to be vacuous in such scenario.
The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a com... more The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.
We explore the possibility of using "weak measurements" without "weak value" for quantum state es... more We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue and recycle the state, unlike for the case of projective measurements. We use this property of weak measurements and design schemes for quantum state estimation for qubits and for Gaussian states. We show, via numerical simulations, that under certain circumstances, our method can outperform the estimation by projective measurements. It turns out that ensemble size plays an important role and the scheme based on recycling works better for small ensembles. A. Von Neumann's measurement model for discrete basis Consider the measurement of an observable A of a quantum system with eigenvectors {|a j } and eigenvalues {a j }, j = 1 • • • n. Imagine an apparatus with continuous pointer positions described by a variable q and its
We introduce local filters as a means to detect the entanglement of bound entangled states which ... more We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurementbased implementation of these filters for 2 ⊗ 2 and 3 ⊗ 3 systems. This provides us with a physical mechanism to implement such local filters.
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and ce... more Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent time evolution and do not explicitly reconstruct the full time-dependent Hamiltonian or interrupt evolution for tomography. Here, we experimentally demonstrate that an a priori unknown, time-dependent Hamiltonian can be reconstructed from continuous weak measurements concurrent with coherent time evolution in a system of two superconducting transmons coupled by a flux-tunable coupler. In contrast to previous work, our technique does not require interruptions, which would distort the recovered Hamiltonian. We introduce an algorithm which recovers the Hamiltonian and density matrix from an incomplete set of continuous measurements and demonstrate that it reliably extracts amplitudes of a variety of single qubit and entangling two qubit Hamiltonians. We further demonstrate how this technique reveals deviations from a theoretical control Hamiltonian which would otherwise be missed by conventional techniques. Our work opens up novel applications for continuous weak measurements, such as studying non-idealities in gates, certifying analog quantum simulators, and performing quantum metrology.
The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", i... more The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissociated from a property of the object, identified with the "grin" of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g., two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit-coupling-like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a so-called confused Cheshire cat. We devise a gedanken experiment in which such a "confusion" can be successfully dissociated from the system, and we find that the dissociation helps in the amplification of signals.
The trade-off between robustness and tunability is a central challenge in the pursuit of quantum ... more The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ and SWAP gates with good estimated fidelities. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate, also with a competitive fidelity. Our protocol applies to multiple fixed-frequency high-coherence platforms, providing a collection of interactions for high-performance quantum information processing. It also establishes the potential of the Floquet framework as a tool for exploring quantum electrodynamics and optimal control.
Based on the statistical concept of the median, we propose a quantum uncertainty relation between... more Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography.
The quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissocia... more The quantum Cheshire cat is a phenomenon in which an object, identified with a "cat", is dissociated from a property of the object, identified with the "grin" of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g. two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit coupling-like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a "confused Cheshire cat". We devise a gedanken experiment in which such a "confusion" can be successfully dissociated from the system, and we find that the dissociation helps in amplification of signals.
We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and... more We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is achieved in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions and bosons.
We experimentally construct a novel three-qubit entangled W-superposition (WW) state on an NMR qu... more We experimentally construct a novel three-qubit entangled W-superposition (WW) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the WW state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party WW state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the WW state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the WW state is interconvertible with the GHZ state, it stores entanglement very differently.
We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and... more We study a quantum Stirling cycle which extracts work using quantized energy levels. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is achieved in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions and bosons.
We explore the possibility of using "weak" measurements to carry out quantum state tomography via... more We explore the possibility of using "weak" measurements to carry out quantum state tomography via numerical simulations. Given a fixed number of copies of identically prepared states of a qubit, we perform state tomography using weak as well as projective measurements. Due to the collapse of the state after measurement, we cannot reuse the state after a projective measurement. If the coupling strength between the quantum system and the measurement device is made weaker, the disturbance caused to the state can be lowered. This then allows us to reuse the same member of the ensemble for further measurements and thus extract more information from the system. However, this happens at the cost of getting imprecise information from the first measurement. We implement this scheme for a single qubit and show that under certain circumstances, it can outperform the projective measurement-based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths, and different ensemble sizes.
The quantum Cheshire Cat is a mysterious phenomenon that temporarily strips a system - a "ca... more The quantum Cheshire Cat is a mysterious phenomenon that temporarily strips a system - a "cat"- of its property - its "grin". A corollary of this effect is the decoupling of two properties of the same system, which we call the grin and the snarl. This can in principle be realized by detecting two components of polarization of a photon in two different arms of an interferometer. We introduce a mechanism by which we can interchange the positions of these two properties. By doing this we uncover a phenomenon that decouples the grin and the snarl, and puts them in their place even before they encounter the mechanism.
Based on the statistical concept of the median, we propose a quantum uncertainty relation between... more Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies in...
Quantum Chesire Cat is a counterintuitive phenomenon that provides a new window into the nature o... more Quantum Chesire Cat is a counterintuitive phenomenon that provides a new window into the nature of the quantum systems in relation to multiple degrees of freedom associated with a single physical entity. Under suitable pre and postselections, a photon (the cat) can be decoupled from its circular polarization (its grin). In this paper, we explore whether the grin without the cat can be teleported to a distant location. This will be a totally disembodied teleportation protocol. Based on the original Quantum Chesire Cat setup, we design a protocol where the circular polarization is successfully teleported between two spatially separated parties even when the photon is not physically present with them. The process raises questions in our understanding about properties of quantum system. In particular it shows that question like ``whose polarization is it'' can prove to be vacuous in such scenario.
The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a com... more The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.
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Papers by Debmalya Das