scholarly journals Entanglement marginal problems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 589
Author(s):  
Miguel Navascués ◽  
Flavio Baccari ◽  
Antonio Acín
Keyword(s):  
Quantum State ◽  
System Size ◽  
Separable Extension ◽  
Translation Invariant ◽  
Time Space ◽  
Marginal Problem ◽  
Spatial Dimensions ◽  
A Chain ◽  
Reduced Density ◽  
Star Configuration

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

scholarly journals Local-measurement-based quantum state tomography via neural networks

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Tao Xin ◽  
Sirui Lu ◽  
Ningping Cao ◽  
Galit Anikeeva ◽  
Dawei Lu ◽  
...  
Keyword(s):  
Neural Network ◽  
Quantum State ◽  
System Size ◽  
Local Information ◽  
Quantum State Tomography ◽  
The Neural Network ◽  
Local Measurements ◽  
State Tomography ◽  
Daunting Challenge ◽  
Reduced Density

AbstractQuantum state tomography is a daunting challenge of experimental quantum computing, even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine-learning method to recover the ground states of $$k$$k-local Hamiltonians from just the local information, where a fully connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems.

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals The Space-Evolution Frame as an Alternative to Space-Time

2021 ◽  
Author(s):  
Xiaonan Du
Keyword(s):  
Proper Time ◽  
World Line ◽  
Time Frame ◽  
Line Length ◽  
Space Time ◽  
Dimensional Euclidean Space ◽  
Time Space ◽  
Minkowski Space Time ◽  
Spatial Dimensions ◽  
New Perspective

Abstract As an alternative to the Minkowski space-time frame, this paper proposes a four-dimensional Euclidean space that combines three spatial dimensions with proper time instead of time. We call this space evolution, in which proper time is interpreted as an evolutionary position and time is considered world line length and absolute. The space-evolution frame provides a new perspective for our understanding of time, space and special relativity. The new frame is self-consistent and compatible to spacial relativity, the Lorentz transform and its predictions could be derived geometrically by simple coordinate rotation.

scholarly journals Walking as a wandering ethic of (re)location: A public ‘pedagogy of hope’

2020 ◽  
pp. 4-19
Author(s):  
Genevieve Blades
Keyword(s):  
Cultural Dimensions ◽  
Public Pedagogy ◽  
Ecological Context ◽  
The Public ◽  
Time Space ◽  
The Social ◽  
Spatial Dimensions ◽  
Temporal And Spatial ◽  
Pedagogy Of Hope

This paper considers the public pedagogy of location in relation to walking. I walk and write withand from my compass orientated to the Freirean notion of a ‘pedagogy of hope’. Using an autoethnographic account of a local walk, walking is (re)presented and interpreted as a wanderingethic of (re)location. Temporal and spatial dimensions of my walking are revealed in the social,cultural and ecological context of the bushfires and the pandemic. Drawing from scholars whotheorize embodiment and the multiple natures of body~time~space, the inter and intra-actionswith/in ecologies are presenced in a sensory narrative. To consider walking as a wandering ethicof (re)location, it is argued that various temporal, spatial, material, historical and cultural dimensions are contingent within the context of change as evident in the aftermath of bushfires and thepandemic. What I examine is the inter-play in relation to what is present and otherwise absentwhilst walking that is interpreted as a ‘pedagogy of hope’ amidst the struggles and uncertaintiesof these times.

scholarly journals All macroscopic quantum states are fragile and hard to prepare

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 118
Author(s):  
Andrea López-Incera ◽  
Pavel Sekatski ◽  
Wolfgang Dür
Keyword(s):  
Quantum State ◽  
Quantum Fisher Information ◽  
System Size ◽  
Quantum States ◽  
Initial State ◽  
Macroscopic Quantum ◽  
Effective System ◽  
Local Observables ◽  
The One ◽  
Arbitrary Quantum

We study the effect of local decoherence on arbitrary quantum states. Adapting techniques developed in quantum metrology, we show that the action of generic local noise processes --though arbitrarily small-- always yields a state whose Quantum Fisher Information (QFI) with respect to local observables is linear in system size N, independent of the initial state. This implies that all macroscopic quantum states, which are characterized by a QFI that is quadratic in N, are fragile under decoherence, and cannot be maintained if the system is not perfectly isolated. We also provide analytical bounds on the effective system size, and show that the effective system size scales as the inverse of the noise parameter p for small p for all the noise channels considered, making it increasingly difficult to generate macroscopic or even mesoscopic quantum states. In turn, we also show that the preparation of a macroscopic quantum state, with respect to a conserved quantity, requires a device whose QFI is already at least as large as the one of the desired state. Given that the preparation device itself is classical and not a perfectly isolated macroscopic quantum state, the preparation device needs to be quadratically bigger than the macroscopic target state.

An observable measure of entanglement for pure states of multi-qubit systems

2003 ◽  
Vol 3 (6) ◽  
pp. 619-626
Author(s):  
G. Brennen
Keyword(s):  
Quantum State ◽  
Physical Quantity ◽  
Optical Lattice ◽  
Efficient Manner ◽  
Quantum State Tomography ◽  
State Tomography ◽  
Pure States ◽  
A Chain ◽  
Full Quantum ◽  
Math Phys

Recently, Meyer and Wallach [Meyer and Wallach (2002), J. of Math. Phys., 43, pp. 4273] proposed a measure of multi-qubit entanglement that is a function on pure states. We find that this function can be interpreted as a physical quantity related to the average purity of the constituent qubits and show how it can be observed in an efficient manner without the need for full quantum state tomography. A possible realization is described for measuring the entanglement of a chain of atomic qubits trapped in a 3D optical lattice.

scholarly journals A complete hierarchy for the pure state marginal problem in quantum mechanics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiao-Dong Yu ◽  
Timo Simnacher ◽  
Nikolai Wyderka ◽  
H. Chau Nguyen ◽  
Otfried Gühne
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Semidefinite Programs ◽  
Marginal Problem ◽  
Separability Problem ◽  
Pure Quantum State ◽  
Maximally Entangled States ◽  
Quantum Error

AbstractClarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

scholarly journals Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field

2018 ◽  
Vol 115 (20) ◽  
pp. 5129-5134 ◽  
Author(s):  
Andrea Maiorano ◽  
Giorgio Parisi
Keyword(s):  
Free Energy ◽  
Spin Glasses ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Dimension ◽  
System Size ◽  
Zero Magnetic Field ◽  
Energy Barriers ◽  
Local Fluctuations ◽  
Spatial Dimensions

We study numerically various properties of the free energy barriers in the Edwards–Anderson model of spin glasses in the low-temperature region in both three and four spatial dimensions. In particular, we investigated the dependence of height of free energy barriers on system size and on the distance between the initial and final states (i.e., the overlap distance). A related quantity is the distribution of large local fluctuations of the overlap in large 3D samples at equilibrium. Our results for both quantities (barriers and large deviations) are in agreement with the prediction obtained in the framework of mean-field theory. In addition, our result supports Dlc=2.5 as the lower critical dimension of the model.

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