# Questions tagged [partial-transpose]

The tag has no usage guidance.

20 questions
Filter by
Sorted by
Tagged with
181 views

### Does a partial transpose always have real eigenvalues?

I am working with a tripartite system, but when I partially transpose the $8\times 8$ density matrix I get two complex eigenvalues. I know the criteria for the positive and negative eigenvalues, but ...
128 views

117 views

### In a bipartite system $AB$, why does the entanglement negativity $\mathcal{N}(\rho^{T_A})$ measure the entanglement between $A$ and $B$?

Consider a system composed of two subsystems $A$ and $B$ living in $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. The density matrix of the system $AB$ is defined to be $\rho$. The entanglement ...
83 views

### Defining dimension of an operator in qutip

My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip? Context: If I have my density operator ...
71 views

### Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
55 views

### Compute the negativity of maximally entangled bipartite states

The entanglement negativity $\mathcal N(\rho)$ of a (bipartite) state $\rho$ is defined as the absolute value of the sum of the negative eigenvalues of the partial transpose of a state, or ...
43 views

### Why does the entanglement negativity equal (in magnitude) the sum of the negative eigenvalues?

The entanglement negativity, introduced in (Vidal and Werner 2002), is defined as $$\mathcal N(\rho) \equiv \frac{\|\rho^{T_B}\|_1-1}{2}.$$ It is mentioned there that this equals the sum of the ...
176 views

### How can I implement partial transpose on a variable in Picos (Python, trying to solve an SDP)?

I try to optimise a quantity via an SDP. I optimise over all PPT measurement operators and hence have the constraints $\Pi_k^{T_B} \succeq 0$ (PPT) for my measurement operators. The part of the code ...
90 views

### Why is $\rho$ NPT if and only if $\rho^{\otimes N}$ is NPT?

In Horodecki et al. (1998), to prove that distillability implies having a negative partial transpose (being NPT). The authors use the fact that "a state $\rho$ is NPT if and only if $\rho^{\otimes N}$ ...
72 views

### Are inseparable states with positive partial transpose nonlocal?

In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, ...
206 views

I'm going through some slides on the PPT/NPT criteria along with Horodecki's paper, and I'm kind of stuck. Let's take this slide: Firstly, why can we write a bipartite density matrix as $\sum_{... 1answer 178 views ### Equivalent determinant condition for Peres-Horodecki criteria The Peres-Horodecki criteria for a 2*2 state states that if the smallest eigenvalue of the partial transpose of the state is negative, it is entangled, else it is separable. According to this paper (... 1answer 71 views ### Structural Physical Approximation of Partial Transpose To make the partial transpose a complete positive and therefore physical map, one has to mix it with enough of the maximally mixed state to offset the negative eigenvalues. The most negative ... 1answer 203 views ### Are entanglement witnesses of this form optimal? One can make an entanglement witness by taking the partial transpose of any pure entangled state. Consider$|\phi \rangle $as any pure entangled state. Then$W = | \phi \rangle \langle \phi |^{T_2} ...
Question: For 2x2 and 2x3 systems, is the partial transpose the only positive but not completely positive operation that is possible? Why this came up: The criteria for detecting if a state $\rho$ is ...
In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators. I know that for a positive trace-preserving operator $\Lambda$ (e.g. the ...