Equivalence of bipartite quantum mixed states under local unitary transformations

Author(s):  
Sergio Albeverio ◽  
Shao-Ming Fei ◽  
Xiao-Hong Wang
2012 ◽  
Vol 19 (02) ◽  
pp. 283-292
Author(s):  
Naihuan Jing

We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed states is independent from the actual values of the eigenvalues and only depends on the multiplicities of the eigenvalues. The interpretation in terms of homogeneous spaces of unitary groups is also discussed.


2011 ◽  
Vol 08 (04) ◽  
pp. 853-883 ◽  
Author(s):  
P. ANIELLO ◽  
J. CLEMENTE-GALLARDO ◽  
G. MARMO ◽  
G. F. VOLKERT

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n) × U(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n = 2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2) × SU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.


2007 ◽  
Vol 05 (06) ◽  
pp. 795-803 ◽  
Author(s):  
ZU-HUAN YU ◽  
XIAN-QING LI-JOST ◽  
SHAO-MING FEI

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.


1996 ◽  
Vol 105 (19) ◽  
pp. 8661-8665 ◽  
Author(s):  
Xiangling Chen ◽  
Guohe Sha ◽  
Bo Jiang ◽  
Jinbao He ◽  
Cunhao Zhang

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Maria Violaris ◽  
Gaurav Bhole ◽  
Jonathan A. Jones ◽  
Vlatko Vedral ◽  
Chiara Marletto
Keyword(s):  

CNS Spectrums ◽  
2016 ◽  
Vol 22 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Minoru Takeshima

The DSM–5 incorporates a broad concept of mixed states and captured ≥3 nonoverlapping symptoms of the opposite polarity using a “with mixed features” specifier to be applied to manic/hypomanic and major depressive episodes. Pharmacotherapy of mixed states is challenging because of the necessity to treat both manic/hypomanic and depressive symptoms concurrently. High-potency antipsychotics used to treat manic symptoms and antidepressants can potentially deteriorate symptoms of the opposite polarity. This review aimed to provide a synthesis of the current evidence for pharmacotherapy of mixed states with an emphasis on mixed mania/hypomania. A PubMed search was conducted for randomized controlled trials (RCTs) that were at least moderately sized, included a placebo arm, and contained information on acute-phase and maintenance treatments of adult patients with mixed episodes or mania/hypomania with significant depressive symptoms. Most studies were post-hoc subgroup and pooled analyses of the data from RCTs for acute manic and mixed episodes of bipolar I disorder; only two prospectively examined efficacy for mixed mania/hypomania specifically. Aripiprazole, asenapine, carbamazepine, olanzapine, and ziprasidone showed the strongest evidence of efficacy in acute-phase treatment. Quetiapine and divalproex/valproate were also efficacious. Combination therapies with these atypical antipsychotics and mood stabilizers can be considered in severe cases. Olanzapine and quetiapine (alone or in combination with lithium/divalproex) showed the strongest evidence of efficacy in maintenance treatment. Lithium and lamotrigine may be beneficial given their preventive effects on suicide and depressive relapse. Further prospective studies primarily focusing on mixed states are needed.


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