MAXIMUM NONLOCAL EFFECTS OF QUANTUM STATES

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1587-1598 ◽  
Author(s):  
SHUANGSHUANG FU ◽  
SHUNLONG LUO
Keyword(s):  
Quantum Correlations ◽  
Quantum Measurements ◽  
Quantum States ◽  
Nonlocal Effect ◽  
Nonlocal Effects ◽  
Bipartite State ◽  
Local Quantum ◽  
Local Measurements ◽  
Minimum Disturbance ◽  
Global And Local

A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.

scholarly journals Quantum Euler Relation for Local Measurements

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 889
Author(s):  
Akram Touil ◽  
Kevin Weber ◽  
Sebastian Deffner
Keyword(s):  
Quantum Systems ◽  
Quantum Measurements ◽  
Weak Coupling Regime ◽  
Local Quantum ◽  
Dissipation Model ◽  
Local Measurements ◽  
Euler Relation ◽  
Quantum Analog ◽  
Back Action ◽  
Classical Thermodynamics

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.

scholarly journals Separation of quantum, spatial quantum, and approximate quantum correlations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 389
Author(s):  
Salman Beigi
Keyword(s):  
Mathematical Model ◽  
Hilbert Spaces ◽  
Quantum Correlations ◽  
Quantum Measurements ◽  
Finite Dimensional ◽  
Nonlocal Correlations ◽  
Local Quantum

Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, i.e., Cq(4,4,2,2)≠Cqs(4,4,2,2). We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, i.e., Cqs(4,4,3,3)≠Cqa(4,4,3,3).

scholarly journals Locally restricted measurements on a multipartite quantum system: data hiding is generic

2015 ◽  
pp. 513-540
Author(s):  
Guillaume Aubrun ◽  
Cecilia Lancien
Keyword(s):  
Quantum System ◽  
Data Hiding ◽  
Quantum Measurements ◽  
Quantum States ◽  
Classical Communication ◽  
Substantial Loss ◽  
Local Measurements ◽  
System Data

We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints, perform in the task of discriminating two multipartite quantum states. We mainly address the following question regarding the behaviour of these distinguishability norms in the highdimensional regime: On a bipartite space, what are the relative strengths of standard classes of locally restricted measurements? We show that the class of PPT measurements typically performs almost as well as the class of all measurements whereas restricting to local measurements and classical communication, or even just to separable measurements, implies a substantial loss. We also provide examples of state pairs which can be perfectly distinguished by local measurements if (one-way) classical communication is allowed between the parties, but very poorly without it. Finally, we study how many POVMs are needed to distinguish almost perfectly any pair of states on C^d, showing that the answer is exp(Θ(d^2 )).

Quantum correlations for two-qubit X states through the local quantum uncertainty

2017 ◽  
Vol 15 (03) ◽  
pp. 1750020 ◽  
Author(s):  
L. Jebli ◽  
B. Benzimoun ◽  
M. Daoud
Keyword(s):  
Quantum Correlations ◽  
Quantum Systems ◽  
Local Observable ◽  
Quantum Metrology ◽  
Quantum Uncertainty ◽  
Bipartite State ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Qubit States ◽  
Spin Coherent States

Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.

scholarly journals Computing conditional entropies for quantum correlations

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Peter Brown ◽  
Hamza Fawzi ◽  
Omar Fawzi
Keyword(s):  
Quantum Key Distribution ◽  
Detection Efficiency ◽  
Conditional Entropy ◽  
Key Distribution ◽  
Quantum Correlations ◽  
Upper Bounds ◽  
Cryptographic Protocols ◽  
Quantum States ◽  
Security Proofs

AbstractThe rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.

scholarly journals Unified entropic measures of quantum correlations induced by local measurements

2016 ◽  
Vol 462 ◽  
pp. 930-939 ◽  
Author(s):  
G.M. Bosyk ◽  
G. Bellomo ◽  
S. Zozor ◽  
M. Portesi ◽  
P.W. Lamberti
Keyword(s):  
Quantum Correlations ◽  
Local Measurements

scholarly journals Local quantum uncertainty as a robust metric to characterize discord-like quantum correlations in subsets of the chromophores in photosynthetic light-harvesting complexes

2020 ◽  
Vol 66 (4 Jul-Aug) ◽  
pp. 525
Author(s):  
M. Chávez-Huerta ◽  
F. Rojas
Keyword(s):  
Quantum Coherence ◽  
Light Harvesting ◽  
Green Sulfur Bacteria ◽  
Quantum Correlations ◽  
Light Harvesting Complexes ◽  
Thermal Equilibrium State ◽  
Light Harvesting Complex ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum

Green sulfur bacteria is a photosynthetic organism whose light-harvesting complex accommodates a pigment-protein complex called Fenna-Matthews-Olson (FMO). The FMO complex sustains quantum coherence and quantum correlations between the electronic states of spatially separated pigment molecules as energy moves with nearly a 100% quantum efficiency to the reaction center. We present a method based on the quantum uncertainty associated to local measurements to quantify discord-like quantum correlations between two subsystems where one is a qubit and the other is a qudit. We implement the method by calculating local quantum uncertainty (LQU), concurrence, and coherence between subsystems of pure and mixed states represented by the eigenstates and by the thermal equilibrium state determined by the FMO Hamiltonian. Three partitions of the seven chromophores network define the subsystems: one chromophore with six chromophores, pairs of chromophores, and one chromophore with two chromophores. Implementation of the LQU approach allows us to characterize quantum correlations that had not been studied before, identify the most quantum correlated subsets of chromophores, and determine that, in the strongest associations of chromophores, the LQU is a monotonically increasing function of the coherence.

MEASURE ENTANGLEMENT OF BIPARTITE SYSTEM BY A NEW NONLOCAL EFFECT

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4275-4279
Author(s):  
SHAO-YING MENG ◽  
LI-BIN FU ◽  
JIE LIU
Keyword(s):  
Bell Inequality ◽  
The State ◽  
Nonlocal Effect ◽  
Nonlocal Effects ◽  
Final State ◽  
Bipartite System ◽  
Cyclic Operation ◽  
Degree Of Entanglement

The state of a bipartite system may be changed by a cyclic operation applied on one of its subsystem. The change is a nonlocal effect, and can be detected only by measuring the two parts jointly. By employing the Hilbert-Schmidt metric, we can quantify such nonlocal effects via measuring the distance between initial and final state. By making use of the new nonlocal effect we can measure the entanglement of bipartite system. For qubit pair, we show that this measurement is equivalent to degree of entanglement and consists with the Bell inequality.

scholarly journals Complementarity of quantum correlations in cloning and deleting of quantum states

2015 ◽  
Vol 91 (6) ◽  
Author(s):  
Sk Sazim ◽  
Indranil Chakrabarty ◽  
Annwesha Datta ◽  
Arun K. Pati
Keyword(s):  
Quantum Correlations ◽  
Quantum States

scholarly journals Local and Non-Local Invasive Measurements on Two Quantum Spins Coupled via Nanomechanical Oscillations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1078
Author(s):  
Dimitrios Maroulakos ◽  
Levan Chotorlishvili ◽  
Dominik Schulz ◽  
Jamal Berakdar
Keyword(s):  
Quantum Coherence ◽  
Indirect Measurement ◽  
Quantum Spin ◽  
Quantum States ◽  
Spin Interaction ◽  
First Case ◽  
Composite Quantum System ◽  
Local Quantum ◽  
Non Local ◽  
Quantum Spins

Symmetry plays the central role in the structure of quantum states of bipartite (or many-body) fermionic systems. Typically, symmetry leads to the phenomenon of quantum coherence and correlations (entanglement) inherent to quantum systems only. In the present work, we study the role of symmetry (i.e., quantum correlations) in invasive quantum measurements. We consider the influence of a direct or indirect measurement process on a composite quantum system. We derive explicit analytical expressions for the case of two quantum spins positioned on both sides of the quantum cantilever. The spins are coupled indirectly to each others via their interaction with a magnetic tip deposited on the cantilever. Two types of quantum witnesses can be considered, which quantify the invasiveness of a measurement on the systems’ quantum states: (i) A local quantum witness stands for the consequence on the quantum spin states of a measurement done on the cantilever, meaning we first perform a measurement on the cantilever, and subsequently a measurement on a spin. (ii) The non-local quantum witness signifies the response of one spin if a measurement is done on the other spin. In both cases the disturbance must involve the cantilever. However, in the first case, the spin-cantilever interaction is linear in the coupling constant Ω , where as in the second case, the spin-spin interaction is quadratic in Ω . For both cases, we find and discuss analytical results for the witness.

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