QUBIT4MATLAB V4.0: c=concurrence(rho); - File Exchange

Code covered by the BSD License

Highlights from
QUBIT4MATLAB V4.0

E0=ising_classical_ground(B) ising_classical_ground Ground state energy of the classical Ising model
E0=ising_ground(BField,vararg... ising_ground Ground state energy of the quantum Ising model
E0=ising_thermal(BField,T,var... ising_thermal - Internal energy of the Ising model in thermal equilibrium
E0=xy_classical_ground(Jx,Jy,... xy_classical_ground Ground state energy of the classical xy model
F=ising_free(BField,T) ising_free - Free energy of the Ising model in thermal equilibrium
H=heisenberg(varargin) heisenbergp Hamiltonian for the Heisenberg model with periodic BEC
H=heisenberg(varargin) heisenberg Hamiltonian for the Heisenberg model with non-periodic BEC
H=ising(BField,varargin) ising Hamiltonian for the Ising model with non-periodic boundary
H=isingp(BField,varargin) isingp Hamiltonian for the Ising model with periodic BEC
H=spising(BField,varargin) spising Hamiltonian for the Ising model with non-periodic BEC; sparse
H=spising2D(BField,Nx,Ny) spising2D Hamiltonian for the 2D Ising model with aperiodic boundary condition; sparse
H=spisingp(BField,varargin) spisingp Hamiltonian for the Ising model with periodic boundary condition; sparse
Hzz=splattice(op1,op2,Nx,Ny) splattice Lattice Hamiltonian for a 2D spin model with nn interaction with aperiodic
Hzz=splatticep(op1,op2,Nx,Ny) splatticep Lattice Hamiltonian for a 2D spin model with nn interaction with periodic
P=proj_asym(N,varargin) proj_asym Gives the projector to the antisymmetric subspace
P=proj_sym(N,varargin) proj_sym Gives the projector to the symmetric subspace
U=U_CNOT U_CNOT 4x4 unitary matrix realizing a CNOT gate
U=U_H U_H 2x2 unitary matrix realizing a Hadamard gate
U=runitary(varargin); runitary Random unitary
[Jx,Jy,Jz]=su2(d); su2 SU(2) generators for dxd matrices
[difference,U0]=twirl2(rho,va...
[fmin,f123]=optspinsq(rho) optspinsq(rho) Optimal spin squeezing inequalities
[g,stab]=gstate(Gamma)
[m,fa0]=maxsymsep(op,varargin) maxsymsep Maximum for symmetric multi-qubit product states.
[r,difference]=twirl(rho,vara... twirl Twirling
[witness,alpha2,coeff2]=optwi... optwitness Optimal entanglement witness for detecting genuine
b=braket(phi1,varargin) braket Dirac's bra-ket
c=binom(a,b)
c=ccnr(rho) ccnr Computable cross norm - realignment criterion
c=coll(op,varargin) coll Defines a collective operator which is the sum of single-qudit operators.
c=comm(A,B) comm Commutator of two matrices.
c=concurrence(rho); concurrence Compute the concurrence of a two-qubit density matrix.
c=cstate(varargin) cstate Defines a cluster state.
c=rstate(varargin) rcstate Defines a ring cluster state.
c=spcoll(op,varargin) spcoll Defines a collective operator which is the sum of single-qudit
coeff=schmidt(state,list) schmidt Schmidt coefficients of a pure state.
e=ex(op,rho) ex Expectation value of an operator
g=ghzstate(varargin) ghzstate Defines a GHZ state.
gs=grstate(H) grstate Normalized ground state of a Hamiltonian
h=nnchain(a,b,varargin) nnchain Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor
h=nnchainp(a,b,varargin) nnchainp Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor
h=spnnchain(a,b,varargin) spnnchain Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor
h=spnnchainp(a,b,varargin) spnnchainp Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor
k=ketbra(f); ketbra Creating a density matrix from an unnormalized state vector.
k=ketbra2(f); ketbra2 Creating a density matrix from an unnormalized state vector.
m=maxbisep(op1,list,varargin) maxbisep Maximum for biseparable multi-qubit states.
m=maxeig(M); maxeig Maximum eigenvalue of a matrix
m=maxppt(op,list,varargin) maxppt Maximum for multi-qudit states with a positive partial transpose.
m=maxsep(op,varargin) maxsep Maximum for multi-qudit separable states.
m=mineig(M); mineig Minimum eigenvalue of a matrix
m=pkron(matrix,no_of_repeatat...
matrix=reordermat(pattern,var... reordermat Transformation matrix for reordering the qudits according to
matrix=reordermatsp(pattern,v... spreordermat Transformation matrix for reordering the qudits according to
maxoverlap=overlapb(state) overlapb Maximal overlap with biseparable states
mb=maxb(op1,varargin) maxb(op) gives maximum value for
mkron(A,B,varargin) mkron Kronecker (tensor) product of several matrices.
mm=reorder(m,pattern,varargin) reorder Reorder a state vector or a density matrix according to
mm=shiftquditsleft(m,varargin) shiftquditsleft Shift the qudits to the left
mm=shiftquditsright(m,varargi... shiftquditsright Shift the qudits to the right
mm=swapqudits(m,k,l,varargin) swapqudits Swap two qudits of a qudit register
mop=quditop(op,k1,varargin) quditop Operator acting on a qudit of a qudit register
mop=sptwoquditop(op,k1,k2,var... spquditop Operator acting on a given qudit; sparse version
mop=sptwoquditop(op,k1,k2,var... sptwoquditop Operator on given qudits; sparse version
mop=twoquditop(op,k1,k2,varar... twoquditop(op,k1,k2,n) defines an n-qudit quantum operator
neg=negativity(rho,list,varar... negativity Negativity for a qudit register.
obs=orthogobs(d) orthogobs Orthogonal observables for a qudit
op=interact(op1,op2,n1,n2,var... interact Interaction between two qudits
op=paulistr(pstring) paulistr Converts a Pauli string into an operator.
op=spinteract(op1,op2,n1,n2,v... spinteract Interaction between two qudits; sparse version
p=rproduct(varargin) rproduct Random product state vector for a given number of qubits.
pstring=decompose(rho,varargi... decompose Creates a string with the Pauli decomposition of a
q=qsize(matrix,varargin)
r=keep(rho_in,listneg,varargi... keep Reduced density matrix keeping the given qubits.
r=keep_nonorm(rho_in,listneg,... keep_nonorm Reduced density matrix keeping the given qubits.
r=rdmat(varargin) rdmat Random density matrix
r=remove(rho_in,list,varargin) remove Reduced density matrix
rho=BES_Breuer(lambda,d) BES_Breuer Breuer?s two-qudit bound entangled state
rho=BES_Horodecki2x4(b) BES_Horodecki2x4 Horodecki's 2x4 bound entangled state
rho=BES_Horodecki3x3(a) BES_Horodecki3x3 Horodecki's 3x3 bound entangled state
rho=BES_UPB3x3 BES_UPB3x3 3x3 bound entangled state constructed with UPBs
rho=thstate(H,kT) thstate Thermal state of a system with a given Hamiltonian
rhoR=mrealign(rho,list,vararg... mrealign Generalized realignment of a multipartite operator
rhoR=realign(rho) realign Realignment of the bipartite density matrix.
rhoT=pt(rho,list,varargin) pt partial transposition of a density matrix
rhoT=pt_nonorm(rho,list,varar... pt_nonorm partial transposition of a density matrix
rho_noisy=addnoise(rho,p) addnoise Adds white noise to a density matrix.
s=mestate(d) mestate Maximally entangled state
s=mmstate(varargin) mmstate Density matrix for the maximally mixed state
s=printv(v,varargin); printv Prints a state vector in product basis.
s=qeye(varargin) qeye Identity matrix for a given number of qudits.
s=qvec(varargin) qvec Empty state vector for a given number of qudits.
s=rvec(varargin) rvec Random state vector for a given number of qudits.
s=singlet(varargin) singlet Defines a singlet state.
s=smolinstate smolinstate Gives the four-qubit bound entangled state
stab=gstate_stabilizer(Gamma) gstate_stabilizer Gets the generators for the stabilizer of a graph state.
t=trace2(rho)
t=trnorm(A) trnorm Tracenorm of a matrix
v=va(op,rho) va Variance of an operator
vec=reordermat(pattern,vararg... reordervec Transformation vector for reordering the qudits according to
w=bra(v) bra After element-wise conjugation, transforms a vector into a normalized row vector.
w=dstate(e,varargin) dstate Defines a symmetric Dicke state.
w=ket(v) ket Transforms a vector into normalized column vector.
w=nm(v) nm Normalization
w=wstate(varargin)
contents.m
example1.m
example2.m
example3.m
example_maxppt.m
example_optwitness.m
paulixyz.m
su3.m
su3_alternative.m
ver.m
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from QUBIT4MATLAB V4.0 by Geza Toth
MATLAB package for quantum information science and quantum mechanics.

c=concurrence(rho);

% concurrence    Compute the concurrence of a two-qubit density matrix.

function c=concurrence(rho);
  y=[0 -i; +i 0];          
  R=rho*kron(y,y)*conj(rho)*kron(y,y);
  % Real is needed since MATLAB always adds a small imaginary part ...
  e=real(sqrt(eig(R)));
  e=-sort(-e);
  c=max(e(1)-e(2)-e(3)-e(4),0);

Highlights from QUBIT4MATLAB V4.0

Highlights from
QUBIT4MATLAB V4.0